Electronic Circuits and Design

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7 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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Electronic Circuits and Design

-

a potpourri of basic electronic circuits, circuit ideas, and formulae for anyone undertaking
electronic circuit design

http://www.radio
-
electronics.co
m/info/circuits/index.php



The exact configuration of an electronic circuit is not always easy to remember, and even then
there are associated electronic circuit design formulae to calculate the various circuit values. This
section of the Radio
-
Electroni
cs.Com website contains information about basic electronic
circuits, building blocks, along with the relevant formulae to provide a unique reference on the
web for anyone undertaking electronic circuit design.


This section is organi
z
ed by the chief compon
ent in the circuit. Thus a filter using an operation
amplifier would come under the operational amplifier section, and a transistor radio frequency
amplifier would come under the transistors section and a pin diode attenuator would be found in
the diodes s
ection.


Resistor circuits

Resistors are the most widely used components in electronic circuits. Although very simple in
concept they are key
s

to the operation of many circuits. They can be used in a variety of ways to
produce the requ
i
red results.

-

Resis
tors in parallel

-

Resistor attenuator circuits


Resistor capacitor (RC) circuits

RC or resistor capacitor circuits are used in a number of applications and may be used to provide
simple frequency dependent circuits.

-

Twin T notch filter


LC filter circui
ts

Using inductors and capacitors a whole variety of filters can be designed and made. These
include low pass, high pass and band pass filters

-

A basic filter overview

-

Low pass LC filter

-

High pass LC filter

-

Band pass LC filter


Diode circuits

The di
ode is one of the most elementary semiconductor devices. It essential
l
y allows current
though the device in one direction. Using this facet of the diode there are many uses, but there are
also other facets of its nature that enable to be used in other appl
ications as well.

-

Simple PIN diode attenuator and switch

-

Constant impedance pin diode attenuator

-

Power supply current limiter

-

Diode voltage multiplier

-

Single balanced diode mixer

-

Double balanced diode mixer


Transistor circuits

-

Two transistor

amplifier circuit with feedback

-

Transistor active high pass filter

-

Transistor current limiter for power supplies


SCR, Diac and Triac Circuits

SCR over
-
voltage crowbar circuit


Operational amplifier circuits

Operational amplifiers are one of the main
building blocks these days used in analogue
electronics. They are not only easy to use, but they are plentiful, cheap and offer a very high level
of performance.

-

Operational amplifier basics

-

Inverting amplifier

-

High input impedance inverting amplifie
r

-

Non
-
inverting amplifier

-

High pass filter

-

Low pass filter

-

Band pass filter

-

Variable gain amplifier

-

Fixed frequency notch filter

-

Twin T notch filter with variable Q

-

Multi
-
vibrator oscillator

-

Bi
-
stable multi
-
vibrator

-

Comparator

-

Schmitt

trigger


Digital logic circuits

Logic circuits consisting of building blocks including AND and OR and NAND and NOR gates
for the basis of today's digital circuitry that is used in widely in electronics. Trigger, bi
-
stables,
flip flops,

etc
.

are also widel
y sued and can be made up from the basic building blocks.

-

Logic truth table

-

Hints and tips on designing and laying out digital or logic circuits

-

Using inverters to create other functions

-

A divide by two frequency divider using a D
-
type flip
-
flop

-

An R S flip flop using two logic gates

-

An edge triggered R S flip flop using two D types

-

An electronically controlled inverter using an exclusive OR gate


Electrostatic Discharge ESD

Electro Static Discharge (ESD) is important for anyone involved with
electronics. Even small
discharges that would go unnoticed in everyday life can cause large amounts of damage to
electronic circuits. Find out all about it and how to ensure electronic circuits are not affected in
our three page tutorial.

-

Electrostatic D
ischarge ESD (3 pages)




Resistor attenuator circuits

-

for use in radio frequency circuits including receivers and transmitters, etc


Attenuator circuits are used in a variety of radio frequency circuit design applications. The
attenuators reduce the le
vel of the signal and this can be used to ensure that the correct radio
signal level enters another circuit block such as mixer or amplifier so that it is not overloaded. As
such attenuators are widely used by radio frequency circuit designers. While it is

possible to buy
ready made attenuators, it is also easy to make attenuators for many applications. Here a simple
resistor network can be used to make attenuators that provide levels of attenuation up to figures
of 60 dB and at frequency of 1 GHz and more,

provided that care is taken with the construction
and the choice of components.


One important feature that is required for radio frequency applications is that the characteristic
impedance should be maintained. In other words the impedance looking into a
nd out of the
attenuator should be matched to the characteristic impedance of the system.


T and Pi networks

There are two basic formats that can be used for resistive attenuators. They are the T and pi
networks. Often there is little to choose between the
m and the choice is often down to the
preference of the designer.


As the name suggests the "T"section attenuator is in the shape of the letter T with two resistors in
the signal line and one in the centre to ground.




T section attenuator


The two resistor values can be calculated very easily knowing the ratio of the input and output
voltages, Vin and Vout respectively and the chara
cteristic impedance Ro.




The pi section attenuator is in the form of the Greek letter pi and has one in line resistor a
nd a
resistor to ground at the input and the output.




Pi section attenuator


Similarly the values for the pi section attenuator
can be calculated




Practical aspects

It is generally good practice not to attempt to achieve any more than a maximum
of 20 dB
attenuation in any one attenuator section. Even this is possibly a little high. It is therefore
common practice to cascade several sections. When this is done the adjoining resistors can be
combined. In the case of the T section attenuator this si
mply means the two series resistors can be
added together. For the pi section attenuators there are parallel resistors.


When making large value attenuators, great care must be taken to prevent the signal leaking past
the attenuator and reaching the output
. This can result from capacitive or inductive coupling and
poor earth arrangements. To overcome these problems good earth connection and careful layout,
keeping the output and input away from one another are required. It may also be necessary to
place a s
creen between the different sections.


Using these attenuators a surprisingly good frequency response can be obtained. Non
-
inductive
resistors are required to ensure the best performance, and using good printed circuit board
techniques and surface mount re
sistors, a good performance at frequencies in excess of 1 GHz are
easy to achieve.


Table of resistor values for 50 ohm attenuators

Resistor designations refer to diagrams above

Loss in dB

R1

R2

R3

R4

1

2.9

433

870

5.8

2

5.7

215

436

11.6

3

8.
5

142

292

17.6

4

11.3

105

221

23.8

5

14.0

82.2

179

30.4

6

16.6

66.9

151

37.3

7

19.1

55.8

131

44.8

8

21.5

47.3

116

52.8

9

23.8

40.6

105

61.6

10

26.0

35.1

96.2

71.2

11

28.0

30.6

89.2

81.7

12

29.9

26.8

8
3.5

93.2

13

31.7

23.6

78.8

106

14

33.4

20.8

74.9

120

15

34.9

18.4

71.6

136

16

36.3

16.3

68.8

154

17

37.6

14.4

66.5

173

18

38.8

12.8

64.4

195

19

39.9

11.4

62.6

220

20

40.9

10.1

61.1

248



Twin T notch filte
r

-

design and circuit considerations for a resistor capacitor (RC) twin T notch filter


The twin T circuit is very useful as a notch filter. Here the twin T provides a large degree of
rejection at a particular frequency. This notch filter can be useful in

rejecting unwanted signals
that are on a particular frequency. One example may be to filter out unwanted mains hum at 50 or
60 Hz that may be entering a circuit.


The response provided by the filter consists of a low level of attenuation away from the not
ch
frequency. As signals move closer to the notch frequency, the level of attenuation rises, giving
the typical notch filter response. In theory, at the notch frequency the level of attenuation
provided by the twin T notch filter is infinite.




RC
-

Resistor Capacitor Twin T Notch Filter


The circuit for the twin T notch filter is shown above and can be seen to consist of three resistors
a
nd three capacitors. It operates by phase shifting the signals in the different legs and adding
them at the output. At the notch frequency, the signals passing through each leg are 180 degrees
out of phase and cancel out. In theory this provides a complete

null of the signal. However in
practice close tolerance components are required to achieve a good null.


In common with other RC circuits, the RC twin T notch filter circuit has what may be termed as a
soft cut
-
off. The response of the notch circuit falls

away slowly and affects a wide band of
frequencies either side of the cut
-
off frequency. However very close to the cut
-
off frequency the
response falls away very quickly, assuming that close tolerance components have been used.


Calculation of the value f
or the circuit is very straightforward.


fc = 1 / (2 pi R C)


Where:

fc = cut off frequency in Hertz

pi = 3.142

R and C are the values of the resistors and capacitors as in the circuit



Filters overview

-

an overview of the types of filter and the

various design considerations and parameters


Filters of all types are required in a variety of applications from audio to RF and across the whole
spectrum of frequencies. As such filters form an important element within a variety of scenarios,
enabling t
he required frequencies to be passed through the circuit, while rejecting those that are
not needed.


The ideal filter, whether it is a low pass, high pass, or band pass filter will exhibit no loss within
the pass band, i.e. the frequencies below the cut o
ff frequency. Then above this frequency in what
is termed the stop band the filter will reject all signals.


In reality it is not possible to achieve the perfect pass filter and there is always some loss within
the pass band, and it is not possible to achi
eve infinite rejection in the stop band. Also there is a
transition between the pass band and the stop band, where the response curve falls away, with the
level of rejection rises as the frequency moves from the pass band to the stop band.


Filter types

Th
ere are four types of filter that can be defined. These are low pass, high pass, band pass and
band reject filters. As the names indicate, a low pass filter only allows frequencies below what is
termed the cut off frequency through. This can also be though
t of as a high reject filter as it
rejects high frequencies. Similarly a high pass filter only allows signals through above the cut off
frequency and rejects those below the cut off frequency. A band pass filter allows frequencies
through within a given pa
ss band. Finally the band reject filter rejects signals within a certain
band. It can be particularly useful for rejecting a particular unwanted signal or set of signals
falling within a given bandwidth.




Types of filter


Filter frequencies

A filter allows signals through in what is termed the pass band. This is the band of frequencies
below the cut off frequency for the filter.


The c
ut off frequency of the filter is defined as the point at which the output level from the filter
falls to 50% (
-
3 dB) of the in band level, assuming a constant input level. The cut off frequency is
sometimes referred to as the half power or
-
3 dB frequency
.


The stop band of the filter is essentially the band of frequencies that is rejected by the filter. It is
taken as starting at the point where the filter reaches its required level of rejection.


Filter classifications

Filters can be designed to meet a v
ariety of requirements. Although using the same basic circuit
configurations, the circuit values differ when the circuit is designed to meet different criteria. In
band ripple, fastest transition to the ultimate roll off, highest out of band rejection are
some of the
criteria that result in different circuit values. These different filters are given names, each one
being optimi
z
ed for a different element of performance.


Butterworth:

This type of filter provides the maximum in band flatness.


Bessel:

This f
ilter provides the optimum in
-
band phase response and therefore also provides the
best step response.


Chebychev:

This filter provides fast roll off after the cut off frequency is reached. However this
is at the expense of in band ripple. The more in band
ripple that can be tolerated, the faster the
roll off.


Elliptical:

This has significant levels of in band and out of band ripple, and as expected the
higher the degree of ripple that can be tolerated, the steeper it reaches its ultimate roll off.




LC l
ow pass filter

-

the design considerations and formulae (formulas) for an LC (inductor capacitor) low pass filter


Low pass filters are used in a wide number of applications. Particularly in radio frequency
applications, low pass filters are made in their
LC form using inductors and capacitors. Typically
they may be used to filter out unwanted signals that may be present in a band above the wanted
pass band. In this way, this form of filter only accepts signals below the cut
-
off frequency.


Low pass filters

using LC components, i.e. inductors and capacitors are arranged in ether a pi or
T network. For the pi section filter, each section has one series component and either side a
component to ground. The T network low pass filter has one component to ground a
nd either side
there is a series in line component. In the case of a low pass filter the series component or
components are inductors whereas the components to ground are capacitors.




LC Pi and T section low pass filters


There is a variety of different filter variants that can be used dependent upon the requirements in
terms of in band ripple, rate at which final roll off is ach
ieved, etc. The type used here is the
constant
-
k and this produces some manageable equations:


L = Zo / (pi x Fc) Henries


C = 1 / (Zo x pi x Fc) Farads


Fc = 1 / (pi x square root (L x C) Hz


Where

Zo = characteristic impedance in o
hms

C = Capacitance in Farads

L = Inductance in Henries

Fc = Cutoff frequency in Hertz


Further details

In order to provide a greater slope or roll off, it is possible to cascade several low pass filter
sections. When this is done the filter elements from
adjacent sections may be combined. For
example if two T section filters are cascaded and each T section has a 1 uH inductor in each leg
of the T, these may be combined in the adjoining sections and a 2 uH inductor used.


The choice of components for any fi
lter, and in this case for a low pass filter is important. Close
tolerance components should be used to ensure that the required performance is obtained. It is
also necessary to check on the temperature stability to ensure that the filter components do not

vary significantly with temperature, thereby altering the performance.


Care must be taken with the layout of the filter. This should be undertaken not just for the pass
band frequencies, but more importantly for the frequencies in the stop band that may
be well in
excess of the cut off frequency of the low pass filter. Capacitive and inductive coupling are the
main elements that cause the filter performance to be degraded. Accordingly the input and output
of the filter should be kept apart. Short leads an
d tracks should be used, components from
adjacent filter sections should be spaced apart. Screens used where required, and good quality
connectors and coaxial cable used at the input and output if applicable.



LC high pass filter

-

the design considerati
ons and formulae (formulas) for an LC (inductor capacitor) high pass
filter


High pass filters are used in a wide number of applications and particularly in radio frequency
applications. For the radio frequency filter applications, the high pass filters ar
e made from
inductors and capacitors rather than using other techniques such as active filters using operational
amplifiers where applications are normally in the audio range.


High pass filters using LC components, i.e. inductors and capacitors are arrang
ed in ether a pi or
T network. As suggested by its name, the pi network has one series component, and either side of
it there is a component to ground. Similarly the T network high pass filter has one component to
ground and either side there is a series i
n line component. In the case of a high pass filter the
series component or components are capacitors whereas the components to ground are inductors.
In this way these filters pass the high frequency signals, and reject the low frequency signals.
These fil
ters may be used in applications where there are unwanted signals in a band of
frequencies below the cut
-
off frequency and it is necessary to pass the wanted signals in a band
above the cut
-
off frequency of the filter.




LC Pi and T section low pass filters


There is a variety of different filter variants that can be used dependent upon the requirements in
terms of in band ripple
, rate at which final roll off is achieved, etc. The type used here is the
constant
-
k and this produces some manageable equations:


L = Zo / (4 x pi x Fc) Henries


C = 1 / (4 x Zo x pi x Fc) Farads


Fc = 1 / (4 x pi x square root (L
x C) Hz


Where

Zo = characteristic impedance in ohms

C = Capacitance in Farads

L = Inductance in Henries

Fc = Cut off frequency in Hertz


Further details

In order to provide a greater slope or roll off in the high pass filter, it is possible to cascade
sev
eral filter sections. When this is done the filter elements from adjacent sections may be
combined. For example if two T section filters are cascaded and each T section has a 1 uH
inductor in each leg of the T, these may be combined in the adjoining sectio
ns and a 2 uH
inductor used.


The choice of components for any filter, and in this case for a high pass filter is important. Close
tolerance components should be used to ensure that the required performance is obtained. It is
also necessary to check on the

temperature stability to ensure that the filter components do not
vary significantly with temperature, thereby altering the performance.


Care must be taken with the layout of the filter, especially when the filter is used for high
frequencies. Capacitive

and inductive coupling are the main elements that cause the filter
performance to be degraded. Accordingly the input and output of the filter should be kept apart.
Short leads and tracks should be used, Components from adjacent filter sections should be s
paced
apart. Screens used where required, and good quality connectors and coaxial cable used at the
input and output if applicable.




LC band pass filter

-

the design considerations and formulae (formulas) for an LC (inductor capacitor) band pass
filter


Band pass filters using LC components, i.e. inductors and capacitors are used in a number of
radio frequency applications. These filters enable a band of frequencies to be passed through the
filter, while those in the stop band of the band pass filter are

rejected.


These filters are typically used where a small band of frequencies need to be passed through the
filter and all others rejected by the filter.


Like the high pass filters and the low pass filters, there are two topologies that are used for thes
e
filters, namely the Pi and the T configurations. Rather than having a single element in each leg of
the filter as in the case of the low pass and high pass filters, the band pass filter has a resonant
circuit in each leg. These resonant circuits are eith
er series or parallel tuned LC circuits.




LC Pi and T section band pass filters


The equations below provide the values for t
he capacitors and resistors for a constant
-
k filter. As
the filter is a band pass filter there are two cut off frequencies. One at the low edge of the pass
band and the toher at the top edge of the pass band.


L1 = Zo / (pi (f2
-

f1)) Henries


L2 = Zo (f2
-

f1) / (4 pi f2 f1)) Henries


C1 = (f2
-

f1) / (4 pi f2 f1 Zo) Farads


C2 = 1 / (pi Zo (f2
-

f1)) Farads


Zo = characteristic impedance in ohms

C1 and C2 = Capacitance in Farads

L1 and L2 =

Inductance in Henries

f1 and f2 = Cut off frequencies in Hertz


Further details

The choice of components for any filter such as a low pass filter or a high pass filter can be
crucial to its performance. In the case of a band pass filter it is even more im
portant as the circuit
comprises six components rather than just three. As a result of this, close tolerance components
should be used to ensure that the required performance is obtained. It is also necessary to check
on the temperature stability to ensure

that the filter components do not vary significantly with
temperature, thereby altering the performance.


Care must be taken with the layout of the filter, especially when the filter is used for high
frequencies. Capacitive and inductive coupling are the
main elements that cause the filter
performance to be degraded. Accordingly the input and output of the filter should be kept apart.
Short leads and tracks should be used, Components from adjacent filter sections should be spaced
apart. Screens used where
required, and good quality connectors and coaxial cable used at the
input and output if applicable.




Simple PIN diode switch

-

PIN diode attenuator and switch circuit using a single PIN diode


For applications where the ultimate performance is not requi
red a single PIN diode can be used.
The circuit shown only requires a few components and is very simple to implement. Nevertheless
it is able to act as a switch for radio frequency or RF applications and is adequate for many
applications.


When a positive
potential is applied to the control point current, this forward biases the diode and
as a result the radio frequency signal is able to pass through the circuit. When a negative bias is
applied to the circuit, the diode become reverse biased and is effectiv
ely switched off. Under
these conditions the depletion layer in the diode becomes wide and does not allow signal to pass.




Simple PIN diode attenuator and switch


Although in theory any diode could be used in this position, PIN diodes have a number of
advantages as switches. In the first place they are more linear than ordinary PN junction diodes.
This means that
in their action as a radio frequency switch they do not create as many spurious
products. Secondly when reverse biased and switched off, the depletion layer is wider than with
an ordinary diode and this provides for greater isolation when switching.





P
IN diode attenuator

-

a constant impedance attenuator design for radio frequency or RF circuit design applications


Electronically controllable PIN diode attenuators are often used in radio frequency or RF circuit
designs. It is often necessary to be able
to control the level of a radio frequency signal using a
control voltage. It is possible to achieve this using a PIN diode attenuator circuit. Some circuits
do not offer a constant impedance, whereas this PIN diode attenuator gives a satisfactory match.


T
he PIN diode variable attenuator is used to give attenuation over a range of about 20 dB and can
be used in 50 ohm systems. The inductor L1 along with the capacitors C4 and C5 are included to
prevent signal leakage from D1 to D2 that would impair the perfo
rmance of the circuit.


The maximum attenuation is achieved when Vin is at a minimum. At this point current from the
supply V+ turns the diodes D1 and D2 on effectively shorting the signal to ground. D3 is then
reverse biased. When Vin is increased the dio
des D1 and D2 become reverse biased, and D3
becomes forward biased, allowing the signal to pass through the circuit.




PIN diode variable attenuator


Typical values for the circuit might be: +V : 5 volts; Vin : 0
-

6 volts; D1 to D3 HP5082
-
3080
PIN diodes; R1 2k2; R2 : 1k; R3 2k7; L1 is self resonant above the operating frequency, but
sufficient to give isolatio
n between the diodes D1 and D2.


These values are only a starting point for an experimental design, and are only provided as such.
The circuit may not be suitable in all instances.


Choice of diode

Although in theory any diode could be used in this positi
on, PIN diodes have a number of
advantages as switches. In the first place they are more linear than ordinary PN junction diodes.
This means that in their action as a radio frequency switch they do not create as many spurious
products and additionally as a
n attenuator they have a more useful curve. Secondly when reverse
biased and switched off, the depletion layer is wider than with an ordinary diode and this
provides for greater isolation when switching.




Power supply current limiter

-

a simple circuit
for a power supply current limiter using two diodes and a resistor


In any power supply there is always the risk that the output will experience a short circuit.
Accordingly it is necessary to protect the power supply from damage under these circumstances.

There are a number of circuits that can be used for power supply protection, but one of the
simplest circuits uses just two diodes and an additional resistor.


The circuit for the power supply current limiter uses a sense resistor placed in series with th
e
emitter of the output pass transistor. Two diodes placed between the output of the circuit and the
base of the pass transistor provide the current limiting action. When the circuit is operating within
its normal operating range a small voltage exists acr
oss the series resistor. This voltage plus the
base emitter voltage of the transistor is less than the two diode junction drops needed to turn on
the two diodes to allow them to conduct current. However as the current increases so does the
voltage across t
he resistor. When it equals the turn on voltage for a diode the voltage across the
resistor plus the base emitter junction drop for the transistor equals two diode drops, and as a
result this voltage appears across the two diodes, which start to conduct. T
his starts to pull the
voltage on the base of the transistor down, thereby limiting the current that can be drawn.




Ba
sic power supply current limiting circuit


The circuit of this diode current limiter for a power supply is particularly simple. The value of the
series resistor can be calculated so that the voltage across it rises to 0.6 volts (the turn on voltage
for a
silicon diode) when the maximum current is reached. However it is always best to ensure
that there is some margin in hand by limiting the current from the simple power supply regulator
before the absolute maximum level is reached.


Using in other circuits

The same simple diode form of current limiting may be incorporated into power supply circuits
that use feedback to sense the actual output voltage and provide a more accurately regulated
output. If the output voltage sense point is taken after the series c
urrent sensing resistor, then the
voltage drop across this can be corrected at the output.




Power supply with feedbac
k and current limiting


This circuit gives far better regulation than the straight emitter follower regulator. Also voltage
drops in the series current limit sense resistor can be accounted for provided that there is
sufficient voltage drop across the seri
es pass transistor in the power supply circuit. Finally the
output voltage can be adjusted to give the required value using the variable resistor.


Summary

The diode form of current limiting can be incorporated into a power supply circuit very easily.
Addi
tionally it is cheap and convenient. However if superior performance is needed th
e
n a
transistori
z
ed form of current limit may be used. This gives a sharper limiting that is more
suitable for more exacting power supply requirements.



Diode voltage multipl
ier

-
a circuit using diodes that multiplies the incoming voltage


Within a power supply or other rectifier circuit it is possible to configure the diodes in such a way
that they double, triple or more, the level of the incoming voltage. This type of voltag
e multiplier
circuit finds uses in many applications where a low current, high voltage source is required.


Although there are some variations on the basic circuit, these ones shown below use a single
winding on the transformer that is required, one side o
f which can be grounded. Alternatively
another AC source can be used. In this configuration the circuit is particularly convenient as the
AC source does not need to be isolated from ground.




Diode voltage doubler circuit


In this voltage doubler circuit the first diode rectifies the signal and its output is equal to the peak
voltage from the transformer rectified as a
half wave rectifier. An AC signal via the capacitor also
reaches the second diode, and in view of the DC block provided by the capacitor this causes the
output from the second diode to sit on top of the first one. In this way the output from the circuit
is

twice the peak voltage of the transformer, less the diode drops.


Variations of the basic circuit and concept are available to provide a voltage multiplier function
of almost any factor. Applying the same principle of sitting one rectifier on top of anoth
er and
using capacitive coupling enables a form of ladder network to built up.


The voltage multiplier circuits are very useful. However they are normally suitable only for low
current applications. As the voltage multiplication increases the losses increa
se. The source
resistance tends to rise, and loading becomes an issue. For each diode in the chain there is the
usual diode drop (normally 0.6 volts for a silicon diode), but the reactance of the capacitors can
become significant, especially when mains fre
quencies of 50 or 60 Hz are used. High voltage
high value capacitors can be expensive and large. This may provide physical constraints for
making them too large.



Diode single balanced mixer

-
a circuit of a diode single balanced mixer and its typical appl
ications for radio frequency, RF
circuits


Mixers are widely used for radio frequency of RF applications. The mixers used in this arena
multiply the two signals entering the circuit together. (note
-

audio mixers add signals together).
The multiplier type
mixers used in radio frequency applications are formed using non
-
linear
devices. As a result the two signals entering the circuit are multiplied together
-

the output at any
given time is proportional to the product of the levels of the two signals enterin
g the circuit at that
instant. This gives rise to signals at frequencies equal to the sum and the difference of the
frequencies of the two signals entering the circuit.


One of the simpler mixer circuits is based around two diodes. This type of diode known

as a
single balanced diode mixer circuit provides rejection of the input signals at the output as a result
of the fact that the two inputs are balanced.


The circuit is only singly balanced and as a result it does not give isolation between the two input
ports. This means that the signal from the local oscillator may leak onto the signal input line and
this may give rise to inter
-
modulation distortion. However for many applications this circuit
operates quite satisfactorily. Where this may be a problem the
n a double balanced mixer should
be used.




The circuit of a diode single balanced mixer


The circuit has
a typical conversion loss, i.e. the difference between the signal input and the
output of around 8dB, although this depends upon the components used and the construction. The
diodes should be as nearly matched as possible, and the transformer should be clo
sely balanced
for optimum rejection of the input signals at the output.


Where the input signals are widely spaced in frequency, it is possible to utili
z
e a variation of the
basic single balanced diode mixer to good effect. The circuit which is shown below

may be used
in a variety of applications, for example where an audio signal needs to be modulated onto a
radio frequency, RF, carrier. In the circuit the two signals are combined using C1 as a high pass
filter, and the combination of RFC and C2 as a low p
ass filter. In this way the leakage between
the two input ports is minimi
z
ed. A further refinement is that a balance control is incorporated
into the balanced mixer circuit. This is used to ensure optimum balance. For example when used
for modulating an RF

carrier, it can be used to minimi
z
e the level of the carrier at the output,
thereby ensuring only the two sidebands are produced.




The circuit of a diode single balanced mixer with a balance control


Although this form of the single balanced diode mixer circuit does require a few more
components, the performance is improved as the variable resist
or enables much better balance to
be achieved, and additionally there is some form of isolation between the two inputs.



Double balanced diode mixer

-
a circuit of a double balanced diode mixer and its typical applications for radio frequency, RF
circuits


Radio frequency mixers such as the double balanced diode mixer are used, not for adding signals
together as in an audio mixer, but rather multiplying them together. When this occurs the output
is a multiplication of the two input signals, and signals at n
ew frequencies equal to the sum and
difference frequencies are produced.


Being a double balanced mixer, this type of mixer suppresses the two input signals at the output.
In this way only the sum and difference frequencies are seen. Additionally the balan
cing also
isolates the two inputs from one another. This prevents the signals from one input entering the
output circuitry of the other and the resultant possibility of inter
-
modulation.




The circuit of a double balanced diode mixer


Typical performance figures for the circuit are that isolation between ports is around 25 dB, and
the conversion loss, i.e. the

difference between the signal input and output levels is around 8 dB.
Using typical diodes, the input level to the mixer on the local oscillator port is around 1 volt RMS
or 13 dBm into 50 ohms.


The isolation between the various ports is maximi
z
ed if the

coils are accurately matched so that a
good balance is achieved. Additionally the diodes must also be matched. Often they need to be
specially selected to ensure that their properties closely match each other.


In order to obtain the optimum performance t
he source impedances for the two input signals and
the load impedance for the output should be matched to the required impedance. It is for this
reason that small attenuators are often placed in the lines of the mixer. These are typically 3 dB,
and althoug
h they do reduce the signal level they improve the overall performance of the mixer.


These mixers may be constructed, but for many commercial pieces of equipment they are
purchased in a manufactured form. These devices can have the required level of devel
opment and
as a result their performance can be optimi
z
ed. Although they are often not cheap to buy, their
performance is often worth the additional expense.



Simple two transistor amplifier

-

a simple design for a two transistor amplifier with feedback


This electronic circuit design shows a simple two transistor amplifier with feedback. It offers a
reasonabl
e

high impedance while providing a low output impedance. It is an ideal transistor
amplifier circuit for applications where a higher level of gain is

required than that which would
be provided by a single transistor stage.




Two transistor amplifier circuit with f
eedback


Av = (R4 + R5) / R4


The resistors R1 and R2 are chosen to set the base of TR1 to around the mid point. If some
current limiting is required then it is possible to place a resistor between the emitter of TR2 and
the supply.



Tran
sistor high pass filter

-

a simple one transistor circuit to provide an active high pass filter


It is sometimes convenient to design a simple active high pass filter using one transistor. The
transistor filter circuit given below provides a two pole filte
r with unity gain. Using just a single
transistor, this filter is convenient to place in a larger circuit because it contains few components
and does not occupy too much space.


The active high pass transistor circuit is quite straightforward, using just a

total of four resistors,
two capacitors and a single transistor. The operating conditions for the transistor are set up in the
normal way. R2 and R3 are used to set up the bias point for the base of the transistor. The resistor
Re is the emitter resistor
and sets the current for the transistor.


The filter components are included in negative feedback from the output of the circuit to the
input. The components that form the active filter network consist of C1, C2, R1 and the
combination of R2 and R3 in para
llel, assuming that he input resistance to the emitter follower
circuit are very high and can be ignored.




T
ransistor active high pass filter circuit


C1 = 2 C2


R1 = R2 x R3 / (R2 + R3)


This is for values where the effect of the emitter follower transistor itself within the high pass
filter circuit can be ignored, i.e.:


Re (B+1) >> R2
x R3 / (R2 + R3)


fo = 1.414 / (4 pi R1 C2)


Where:

B = the forward current gain of the transistor

fo = the cut
-
off frequency of the high pass filter

pi = the
G
reek letter pi and is equal to 3.14285


The equations for determining the component valu
es provide a Butterworth response, i.e.
maximum flatness within the pass
-
band at the expense of achieving the ultimate roll off as
quickly as possible. This has been chosen because this form of filter suits most applications and
the mathematics works out e
asily




Over
-
voltage crowbar circuit

-

an over voltage crowbar protection circuit using a silicon controlled rectifier or SCR


Power supplies are normally reliable, but if they fail then they can cause significant damage to
the circuitry they supply on s
ome occasions. The SCR over
-
voltage crowbar protection circuit
described provides a very simple but effective method of protecting against the certain types of
power supply failure.


In most analogue power supply arrangements a control voltage is fed into
a series regulating
device such as a transistor. This controls the current and hence the output voltage. Typically the
input voltage to this may be well in excess of the output voltage. If the series regulator transistor
in the power supply fails and goes
short circuit, then the full input voltage will appear on the
circuitry that is being supplied and significant damage may result. To overcome this SCR over
voltage crowbar circuits are widely used. These over
-
voltage protection circuits are easy to
design,

simple to construct and may prevent significant levels of damage in the unlikely event of
a power supply failure.


By looking at the voltages involved it is very easy to see why the inclusion of over
-
voltage
protection is so important. A typical supply ma
y provide 5 volts stabili
z
ed to logic circuitry. To
provide sufficient input voltage to give adequate stabili
z
ation, ripple rejection and the like, the
input to the power supply regulator may be in the region of 10 to 15 volts. Even 10 volts would
be suffi
cient to destroy many chips used today, particularly the more expensive and complicated
ones. Accordingly preventing this is of great importance.


Circuit

Most good bench power supplies include a form of over
-
voltage protection, but for those power
supplie
s or for other applications where over voltage protection is required, a simple over voltage
crowbar circuit can be built. It uses just four components: a silicon controlled rectifier or SCR, a
zener diode, a resistor and a capacitor.




SCR over
-
voltage crowbar circuit


The SCR over voltage crowbar or protection circuit is connected between the output of the power
sup
ply and ground. The zener diode voltage is chosen to be slightly above that of the output rail.
Typically a 5 volt rail may run with a 6.2 volt zener diode. When the zener diode voltage is
reached, current will flow through the zener and trigger the silico
n controlled rectifier or
thyristor. This will then provide a short circuit to ground, thereby protecting the circuitry that is
being supplied form any damage.


As a silicon controlled rec
t
ifier, SCR, or thyristor is able to carry a relatively high current

-

even
quite average devices can conduct five amps and short current peaks of may be 50 and more
amps, cheap devices can provide a very good level of protection for small cost. Also voltage
across the SCR will be low, typically only a volt when it has fir
ed and as a result the heat sinking
is not a problem.


However it is necessary to ensure that the power supply has some form of current limiting. Often
a fuse is ideal because the SCR will be able to clamp the voltage for long enough for it to blow.


The s
mall resistor, often around 100 ohms from the gate of the thyristor or SCR to ground is
required so that the zener can supply a reasonable current when it turns on. It also clamps the gate
voltage at ground potential until the zener turns on. The capacitor

is present to ensure that short
spikes to not trigger the circuit. Some optimi
z
ation may be required in choosing the correct value
although 0.1 microfarads is a good starting point.


Limitations

Although this power supply over
-
voltage protection circuit i
s widely used, it does have some
limitations. Most of these are associated with the zener diode. The zener diode is not adjustable,
and these diodes come with at best a 5% tolerance. In addition to this the firing voltage must be
sufficiently far above the

nominal power supply output voltage to ensure that any spikes that may
appear on the line do not fire the circuit. When taking into account all the tolerances and margins
the guaranteed voltage at which the circuit may fire can be 20
-

40% above the nomin
al
dependent upon the voltage of the power supply. The lower the voltage the greater the margins
needed. Often on a 5 volt supply there can be difficulty designing it so that the over
-
voltage
crowbar fires below 7 volts where damage may be caused to circui
ts being protected.


It is also necessary to ensure that there is some means of limiting the current should the over
-
voltage crowbar circuit fire. If not then further damage may be caused to the power supply itself.
Often a fuse may be employed in the circ
uit. In some circuits a fuse is introduced prior to the
series regulator transistor, and the SCR anode connected to the junction node where the output of
the fuse is connected to the input of the series regulator. This ensures that the fuse will blow
swift
ly.


Despite its drawbacks this is still a very useful circuit which can be used in a variety of areas.



Operational amplifier basics

-

Overview of the operational amplifier or op
-
amp as a circuit building block


Operational amplifiers are one of the work
horses of the analogue electronics scene. They are
virtually the ideal amplifier, providing a combination of a very high gain, a very high input
impedance and a very low output impedance. The input to the operational amplifier has
differential inputs, and
these enable the operational amplifier circuit to be used in an enormous
variety of circuits.


The circuit symbol for an operational amplifier consists simply of a triangle as shown below. The
two inputs are designated by "+" and "
-
" symbols, and the outpu
t of the operational amplifier is at
the opposite end of the triangle. Inputs from the "+" input appear at the output in the same phase,
whereas signals present at the "
-
" input appear at the output inverted or 180 degrees out of phase.
This gives rise to
the names for the inputs. The "+" input is known as the non
-
inverting input,
while the "
-
" input is the inverting input of the operational amplifier.




Operational amplifier circuit symbol


Often the power supply rails for the operational amplifier are not shown in circuit diagrams and
there is no connection for a ground line. The power rails for the operational amplifier are
assum
ed to be connected. The power for the operational amplifier is generally supplied as a
positive rail and also a negative rail. Often voltages of +15V and
-
15 V are used, although this
will vary according to the application and the actual chip used.


The ga
in of the operational amplifier is very high. Figures for the levels of gain provided by an
operational amplifier on its own are very high. Typically they may be upwards of 10 000.


While levels of gain may be too high for use on their own, the application

of feedback around the
operational amplifier enables the circuit to be used in a wide variety of applications, from very
flat amplifiers, to filters, oscillators, switches, and much more.


Open loop gain

The gain of an operational amplifier is exceedingly

high. Normally feedback is applied around
the op
-
amp so that the gain of the overall circuit is defined and kept to a figure which is more
usable. However the very high level of gain of the op
-
amp enables considerable levels of
feedback to be applied to e
nable the required performance to be achieved.


When measured the open loop gain of an operational amplifier falls very rapidly with increasing
frequency. Typically an op
-
amp may have an open loop gain of around 10^5, but this usually
starts to fall very q
uickly. For the famous 741 operational amplifier, it starts to fall at a frequency
of only 10 Hz.


Slew rate

With very high gains the operational amplifiers have what is termed compensation capacitance to
prevent oscillation. This capacitance combined wit
h the limited drive currents mean that the
output of the amplifier is only able to change at a limited rate, even when a large or rapid change
occurs at the input. This maximum speed is known as the slew rate. A typical general purpose
device may have a sl
ew rate of 10 V / microsecond. This means that when a large step change is
placed on the input, the device would be able to provide an output 10 volt change in one
microsecond.


The figures for slew rate change are dependent upon the type of operational am
plifier being used.
Low power op
-
amps may only have a slew rate of a volt per microsecond, whereas there are fast
operational amplifiers capable to providing slew rates of 1000 V / microsecond.


The slew rate can introduce distortion onto a signal by limit
ing the frequency of a large signal
that can be accommodated. It is possible to find the maximum frequency or voltage that can be
accommodated. A sine wave with a frequency of f Hertz and amplitude V volts requires an
operational amplifier with a slew rate

of 2 x pi x V x V volts per second.


Offset null

One of the minor problems with an operational amplifier is that they have a small offset.
Normally this is small, but it is quoted in the datasheets for the particular operational amplifier in
question. It
is possible to null this using an external potentiometer connected to the three offset
null pins.



Inverting operational amplifier circuit

-

the use of an operational amplifier or op
-
amp in an inverting amplifier or virtual earth circuit


Operational ampl
ifiers can be used in a wide variety of circuit configurations. One of the most
widely used is the inverting amplifier configuration. It offers many advantages from being very
simple to use, requiring just the operational amplifier integrated circuit and a

few other
components.


Basic circuit

The basic circuit for the inverting operational amplifier circuit is shown below. It consists of a
resistor from the input terminal to the inverting input of the circuit, and another resistor
connected from the output
to the inverting input of the op
-
amp. The non inverting input is
connected to ground.




Basic inverting operational amplifier circ
uit


In this circuit the non inverting input of the operational amplifier is connected to ground. As the
gain of the operational amplifier itself is very high and the output from the amplifier is a matter
of a few volts, this means that the difference bet
ween the two input terminals is exceedingly
small and can be ignored. As the non
-
inverting input of the operational amplifier is held at
ground potential this means that the inverting input must be virtually at earth potential (i.e. a
virtual earth).


As t
he input to the op
-
amp draws no current this means that the current flowing in the resistors
R1 and R2 is the same. Using ohms law Vout /R2 =
-
Vin/R1. Hence the voltage gain of the
circuit Av can be taken as:


Av =
-

R2 / R1


As an example, an
amplifier requiring a gain of ten could be built by making R2 47 k ohms and
R1 4.7 k ohms.


Input impedance

It is often necessary to know the input impedance of a circuit. A circuit with a low input
impedance may load the output of the previous circuit and

may give rise to effects such as
changing the frequency response if the coupling capacitors are not large.


It is very simple to determine the input impedance of an inverting operational amplifier circuit. It
is simply the value of the input resistor R1.
This is because the inverting input is at earth potential
(i.e. a virtual earth) and this means that the resistor is connected between the input and earth.



High impedance inverting op amp circuit

-

a high input impedance version of the inverting operatio
nal amplifier or op
-
amp circuit


The standard inverting amplifier configuration is widely used with operational amplifier
integrated circuits. It has many advantages: being simple to construct; it offers the possibility of
summation or mixing (in the audio

sense) of several signals; and of course it inverts the signal
which can be important in some instances.


However the circuit does have some drawbacks which can be important on some occasions. The
main drawback is its input impedance. To show how this can

be important it is necessary to look
at the circuit and take some examples. The basic circuit for the inverting operational amplifier
circuit is shown below. It consists of a resistor from the input terminal to the inverting input of
the circuit, and anot
her resistor connected from the output to the inverting input of the op
-
amp.
The non inverting input is connected to ground.




Basic inverting operational amplifier circuit


The gain for the amplifier can be calculated from the formula:


Av =
-

R2 / R1


If a high gain of, for example 100, is required this means that the ratio of R2 : R1 is 100. It is
good
practice to keep the resistors in op amp circuits within reasonable bounds. In view of this
the maximum value for R2 should be 1 M Ohm. This means that the input resistor and hence the
input resistance to the amplifier circuit as a whole is 10 k Ohm. In so
me instances this may not be
sufficiently high.


To overcome this problem it is possible to modify the circuit, and add a couple of extra resistors.
The feedback resistor R2 serves to limit the amount of feedback. The higher it is the less
feedback, and he
nce the higher the gain. By adding a couple of additional resistors across the
output to act as a potential divider and taking the resistor R2 from the centre point, the level of
feedback can be reduced. The circuit for this configuration is shown below:




High input impedance inverting operational amplifier circuit


The gain for this amplifier can be calcula
ted from the formula:


Av =
-

R2 (R3 + R4) / (R1 x R4)


Again the input resistance is equal to R1, but this can be made higher for the same gain.


Reminder

It is worth mentioning at this point that for high levels of gain, the gain bandwidth pr
oduct of the
basic op amp itself may become a problem. With levels of gain of 100, the bandwidth of some
operational amplifier ICs may only be around 3 kHz. Check the data sheet for the given chip
being used before settling on the level of gain.



Non
-
inve
rting operational amplifier circuit

-

the use of an operational amplifier or op
-
amp in a non
-
inverting amplifier circuit


Operational amplifiers can be used in two basic configurations to create amplifier circuits. One is
the inverting amplifier where the
output is the inverse or 180 degrees out of phase with the input,
and the other is the non
-
inverting amplifier where the output is in the same sense or in phase with
the input.


Both operational amplifier circuits are widely used and they find applications

in different areas.
When an operational amplifier or op
-
amp is used as a non
-
inverting amplifier it only requires a
few additional components to create a working amplifier circuit.


Basic circuit

The basic non
-
inverting operational amplifier circuit is sh
own below. In this circuit the signal is
applied to the non
-
inverting input of the op
-
amp. However the feedback is taken from the output
of the op
-
amp via a resistor to the inverting input of the operational amplifier where another
resistor is taken to gro
und. It is the value of these two resistors that govern the gain of the
operational amplifier circuit.




Basic non
-
inverti
ng operational amplifier circuit


The gain of the non
-
inverting circuit for the operational amplifier is easy to determine. The
calculation hinges around the fact that the voltage at both inputs is the same. This arises from the
fact that the gain of the
amplifier is exceedingly high. If the output of the circuit remains within
the supply rails of the amplifier, then the output voltage divided by the gain means that there is
virtually no difference between the two inputs.


As the input to the op
-
amp draws
no current this means that the current flowing in the resistors
R1 and R2 is the same. The voltage at the inverting input is formed from a potential divider
consisting of R1 and R2, and as the voltage at both inputs is the same, the voltage at the invertin
g
input must be the same as that at the non
-
inverting input. This means that Vin = Vout x R1 / (R1
+ R2)

Hence the voltage gain of the circuit Av can be taken as:


Av = 1 + R2 / R1


As an example, an amplifier requiring a gain of eleven could b
e built by making R2 47 k ohms
and R1 4.7 k ohms.


Input impedance

It is often necessary to know the input impedance of a circuit. The input impedance of this
operational amplifier circuit is very high, and may typically be well in excess of 10^7 ohms. For

most circuit applications this can be completely ignored. This is a significant difference to the
inverting configuration of an operational amplifier circuit which provided only a relatively low
impedance dependent upon the value of the input resistor.


A
C coupling

In most cases it is possible to DC couple the circuit. However in this case it is necessary to ensure
that the non
-
inverting has a DC path to earth for the very small input current that is needed. This
can be achieved by inserting a high value r
esistor, R3 in the diagram, to ground as shown below.
The value of this may typically be 100 k ohms or more. If this resistor is not inserted the output
of the operational amplifier will be driven into one of the voltage rails.




Basic non
-
inverting operational amplifier circuit with capacitor coupled input


When inserting a resistor in this manner it should be rememb
ered that the capacitor
-
resistor
combination forms a high pass filter with a cut
-
off frequency. The cut off point occurs at a
frequency where the capacitive reactance is equal to the resistance.



Operational amplifier high pass filter

-
a summary of operat
ional amplifier or op
-
amp active high pass filter circuitry


Operational amplifiers lend themselves to being used for active filter circuits, including a high
pass filter circuit. Using a few components they are able to provide high levels of performance.


The simplest circuit high pass filter circuit using an operational amplifier can be achieved by
placing a capacitor in series with one of the resistors in the amplifier circuit as shown. The
capacitor reactance increases as the frequency falls, and as a r
esult this forms a CR low pass filter
providing a roll off of 6 dB per octave. The cut off frequency or break point of the filter can be
calculated very easily by working out the frequency at which the reactance of the capacitor equals
the resistance of th
e resistor. This can be achieved using the formula:


Xc = 2 pi f C


where:

Xc is the capacitive reactance in ohms

pi is the
G
reek letter and equal to 3.142

f is the frequency in Hertz

C is the capacitance in Farads




Operational ampli
fier circuits with low frequency roll off


Two pole low pass filter

Although it is possible to design a wide variety of filters with different levels of gain and
different roll off patterns using operational amplifiers, the filter described on this page wi
ll give a
good sure
-
fire solution. It offers unity gain and a Butterworth response (the flattest response in
band, but not the fastest to achieve ultimate roll off out of band).




Operational amplifier two pole high pass filter

Simple sure fire design wi
th Butterworth response and unity gain


The calculations for the circuit values are very straightforward for the Butterworth response and
unity gain scenario. Critical damping is required for the circuit and the ratio of the resistor vales
determines this.




When choosing the values, ensure that the resistor values fall in the region between 10 k ohms
and 100 k ohms. This is advisable because the output impedance of the circuit rises with
increasing frequency and values outside this region may affect he p
erformance.



Operational amplifier band pass filter

-
a sure fire operational amplifier or op
-
amp active band pass filter circuit


The design of band pass filters can become very involved even when using operational
amplifiers. However it is possible to si
mplify the design equations while still being able to retain
an acceptable level of performance of the operational amplifier filter for many applications.




Circuit of the operational amplifier active band pass filter




As only one operational amplifi
er is used in the filter circuit, the gain should be limited to five or
less, and the Q to less than ten. In order to improve the shape factor of the operational amplifier
filter one or more stages can be cascaded. A final point to note is that high stabil
ity and tolerance
components should be used for both the resistors and the capacitors. In this way the performance
of the operational amplifier filter will be obtained.


Op
-
amp variable gain amplifier

-

a variable gain circuit using an operational amplifie
r


A useful variable gain and sign amplifier can be constructed using a single variable gain
amplifier. The circuit uses a single operational amplifier, two resistors and a variable resistor.




Variable gain operational amplifier circuit


Using this circuit the gain can be calculated from the formula below. In this the variable "a"
represents the percentage of travel of t
he potentiometer, and it varies between "0" and "1". It is
also worth noting that the input impedance is practically independent of the position of the
potentiometer, and hence the gain


Op amp notch filter

-

the circuit and design considerations for a not
ch filter using an operational amplifier, four
resistors and two capacitors


This operational amplifier notch filter circuit is simple yet effective, providing a notch on a
specific fixed frequency. It can be used to notch out or remove a particular freque
ncy that may
need to be removed.


Having a fixed frequency, this operational amplifier, op amp, notch filter circuit may find
applications such as removing fixed frequency interference like mains hum, from audio circuits.




Active operational amplifier n
otch filter circuit


The circuit is quite straightforward to build. It employs both negative and positive feedback
around the operational amplifier chip and in this way it is able to provide a high degree of
performance.


Calculation of the value for the
circuit is very straightforward. The formula to calculate the
resistor and capacitor values for the notch filter circuit is:


fnotch = 1 / (2 pi R C)


R = R3 = R4


C = C1 = C2


Where:

fnotch = centre frequency of th
e notch in Hertz

pi = 3.142

R and C are the values of the resistors and capacitors in Ohms and Farads


When building the circuit, high tolerance components must be used to obtain the best
performance. Typically they should be 1% or better. A notch depth of

45 dB can be obtained
using 1% components, although in theory it is possible for the notch to be of the order of 60 dB
using ideal components. R1 and R2 should be matched to within 0.5% or they may be trimmed
using parallel resistors.


A further item to e
nsure the optimum operation of the circuit is to ensure that the source
impedance is less than about 100 ohms. Additionally the load impedance should be greater than
about 2 M Ohms.


The circuit is often used to remove unwanted hum from circuits. Values fo
r a 50 Hz notch would
be: C1, C2 = 47 nF, R1, R2 = 10 k, R3, R4 = 68 k.




Op amp twin T notch filter

-

the circuit and design considerations for a twin T notch filter with variable Q using an
operational amplifier


The twin T notch filter is a simple cir
cuit that can provide a good level of rejection at the "notch"
frequency. The simple RC notch filter can be placed within an operational amplifier circuit to
provide an active filter. In the circuit shown below, the level of Q of the notch filter can be
va
ried.




Active twin T notch filter circuit with variable Q



Calculation of the value for the circuit is very straightforward. The formula is the same as that
used for the passive version of the twin T notch filter.


fc = 1 / (2 pi R C)


Where:

f
c = cut off frequency in Hertz

pi = 3.142

R and C are the values of the resistors and capacitors as in the circuit


The notch filter circuit can be very useful, and the adjustment facility for the Q can also be very
handy. The main drawback of the notch fi
lter circuit is that as the level of Q is increased, the
depth of the null reduces. Despite this the notch filter circuit can be successfully incorporated into
many circuit applications.



Operational amplifier multi
-
vibrator

-

a simple multi
-
vibrator osci
llator circuit using a single op amp


It is possible to construct a very simple multi
-
vibrator oscillator circuit using an operational
amplifier. The circuit can be used in a variety of applications where a simple square wave
oscillator circuit is required
.


The circuit comprises two sections. The feedback to the capacitor is provided by th
e resistor R1,
whereas hysteris
es

is provided by the two resistors R2 and R3.




Operational amplifier multi
-
vibrator oscillator


The time period for the oscillation is

provided by the formula:


T = 2 C R1 loge (1 + 2 R2 / R3)


Although many multi
-
vibrator circuits may be provided using simple logic gates, this circuit ahs
the advantage that it can be used to provide an oscillator that will generate a much higher output
than that which could come from a logic circuit running from a 5 volt supply. In addition to this
the multi
-
vibrator oscillator circuit is very simple, requiring just one operational amplifier ( op
amp ), three resistors, and a single capacitor.



Operatio
nal amplifier bi
-
stable multi
-
vibrator

-

a circuit for a bi
-
stable multi
-
vibrator using an operational amplifier, op amp


It is easy to use an operational amplifier as a bi
-
stable multi
-
vibrator. An incoming waveform is
converted into short pulses and thes
e are used to trigger the operational amplifier to change
between its two saturation states. To prevent small levels of noise triggering the circuit, hysteresis
is introduced into the circuit, the level being dependent upon the application required. The
op
erational amplifier bi
-
stable multi
-
vibrator uses just five components, the operational amplifier,
a capacitor and three resistors.




Bi
-
stable multi
-
vibrator operational amplifier circuit


The bi
-
stable circuit has two stable states. These are the posi
tive and negative saturation voltages
of the operational amplifier operating with the given supply voltages. The circuit can then be
switched between them by applying pulses. A negative going pulse will switch the circuit into the
positive saturation volta
ge, and a positive going pulse will switch it into the negative state.




Waveforms for the bi
-
stable multi
-
vibrator operational amplifier circuit


It is very easy to calculate the points at which the circuit will trigger. The positive going pulses
need
to be greater than Vo
-
Sat through the potential divider, i.e. Vo
-
Sat x R3 / (R2 + R3), and
similarly the negative going pulses will need to be greater than Vo+Sat through the potential
divider, i.e. Vo+Sat x R3 / (R2 + R3). If they are not sufficiently lar
ge then the bi
-
stable will not
change state.



Operational amplifier comparator

-

a simple comparator circuit using a single op amp


Comparator circuits find a number of applications in electronics. As the name implies they are
used to compare two voltages
. When one is higher than the other the comparator circuit output is
in one state, and when the input conditions are reversed, then the comparator output switches.


These circuits find many uses as detectors. They are often used to sense voltages. For exam
ple
they could have a reference voltage on one input, and a voltage that is being detected on another.
While the detected voltage is above the reference
,

the output of the comparator will be in one
state. If the detected voltage falls below the reference t
hen it will change the state of the
comparator, and this could be used to flag the condition. This is but one example of many for
which comparators can be used.


In operation the op amp goes into positive or negative saturation dependent upon the input
vol
tages. As the gain of the operational amplifier will generally exceed 100 000 the output will
run into saturation when the inputs are only fractions of a mi
l
li
-
volt apart.


Although op amps are widely used as comparator, special comparator chips are often
used. These
integrated circuits offer very fast switching times, well above those offered by most op
-
amps that
are intended for more linear applications. Typical slew rates are in the region of several thousand
volts per microsecond, although more often fi
gures of propagation delay are quoted.


A typical comparator circuit will have one of the inputs held at a given voltage. This may often
be a potential divider from a supply or reference source. The other input is taken to the point to
be sensed.




Circu
it for a basic operational amplifier comparator


There are a number of points to remember when using comparator circuits. As there is no
feedback the two inputs to the circuit will be at different voltages. Accordingly it is necessary to
ensure that the ma
ximum differential input is not exceeded. Again as a result of the lack of
feedback the load will change. Particularly as the circuit changes there will be a small increase in
the input current. For most circuits this will not be a problem, but if the sour
ce impedance is high
it may lead to a few unusual responses.


The main problem with this circuit is that new the changeover point, even small amounts of noise
will cause the output to switch back and forth. Thus near the changeover point there may be
sever
al transitions at the output and this may give rise to problems elsewhere in the overall
circuit. The solution to this is to use a Schmitt Trigger as described on another page.




Operational amplifier Schmitt trigger

-

a simple circuit using an op amp to

produce a Schmitt trigger to remove multiple transitions on
slow input signals


Although the simple comparator circuit using either an ordinary operational amplifier (op
-
amp)
or a special comparator chip is often adequate, if the input waveform is slow or

has noise on it,
then there is the possibility that the output will switch back and forth several times during the
switch over phase as only small levels of noise on the input will cause the output to change. This
may not be a problem in some circumstance
s, but if the output from the operational amplifier
comparator is being fed into fast logic circuitry, then it can often give rise to problems.


The problem can be solved very easily by adding some positive feedback to the operational
amplifier or comparat
or circuit. This is provided by the addition of R3 in the circuit below and
the circuit is known as a Schmitt trigger.




Operational amplifier
(
Schmitt trigger circuit
)



The effect of the new resistor (R3) is to give the circuit different switching thre
sholds dependent
upon the output state of the comparator or operational amplifier. When the output of the
comparator is high, this voltage is fed back to the non
-
inverting input of the operational amplifier
of comparator. As a result the switching threshol
d becomes higher. When the output is switched
in the opposite sense, the switching threshold is lowered. This gives the circuit what is termed
hysteresis.


The fact that the positive feedback applied within the circuit ensures that there is effectively a
higher gain and hence the switching is faster. This is particularly useful when the input waveform
may be slow. However a speed up capacitor can be applied within the Schmitt trigger circuit to
increase the switching speed still further. By placing a capac
itor across the positive feedback
resistor R3, the gain can be increased during the changeover, making the switching even faster.
This capacitor, known as a speed up capacitor may be anywhere between 10 and 100 pF
dependent upon the circuit.


It is quite e
asy to calculate the resistors needed in the Schmitt trigger circuit. The centre voltage
about which the circuit should switch is determined by the potential divider chain consisting of
R1 and R2. This should be chosen first. Then the feedback resistor R3
can be calculated. This
will provide a level of hysteresis that is equal to the output swing of the circuit reduced by the
potential divide formed as a result of R3 and the parallel combination of R1 and R2.



Logic gate truth table

-

used for AND, NAND, O
R, NOR and exclusive OR functions in electronic logic gate circuits


Logic circuits form the very basis of digital electronics. Circuits including the AND, NAND, OR,
NOR and exclusive OR gates or circuits form the building blocks on which much of digital
e
lectronics is based.


The various types of electronic logic gates that can be used have outputs that depend upon the
states of the two (or more) inputs to the logic gate. The two main types are AND and OR gates,
although there are logic gates such as exclu
sive OR gates and simple inverters.


For the explanations below, the logic gates have been assumed to have two inputs. While two
input gates are the most common, many gates that possess more than two inputs are used. The
logic in the explanations below can

be expanded to cover these multiple input gates, although for
simplicity the explanations have been simplified to cover two input cases.


AND and NAND gates

An AND gate has an output that is a logical "1" or high when a "1" is present at both inputs. In
o
ther words if a logic gate has inputs A and B, then the output to the circuit will be a logical "1"
when A AND B are at level "1". For all other combinations of input the output will be at "0".


A NAND gate is simply an AND gate with its output inverted. I
n other words the output is at
level "0" when A AND B are at "1". For all other states the output is at level "1".


OR and NOR gates

For an electronic OR gates the output is at "1" when the input at either A or B is at logical "1". In
other words only one

of the inputs has to be at "1" for the output to be set to "1". The output
remains at "1" even if both inputs are at "1". The output only goes to "0" if no inputs are at "1".


In just the same way that a NAND gate is an AND gate with the output inverted,
so too the NOR
gate is an OR gate with its output inverted. Its output goes to "0" when either A OR B is at
logical "1". For all other input states the output of the NOR gate goes to "1".


Exclusive OR

One other form of OR gate that is often used is known
as an exclusive OR gate. As the name
suggests it is a form of OR gate, but rather than providing a "1" at the output for a variety of input
conditions as in the case of a normal OR gate, the exclusive OR gate only provides a "1" when
one of its inputs is a
t "1", and not both (or more than one in the case of a gate with more than two
inputs).


Inverter

The final form of gate, if indeed it could be categori
z
ed as a gate is the inverter. As the name
suggests this circuit simply inverts the state of the input s
ignal. For an input of "0" it provides an
output of "1" and for an input of "1", it provides an output of "0". Although very simple in its
operation, these circuits are often of great use, and accordingly they are quite widely used.

Logic gate truth table

A

B

AND

NAND

OR

NOR

Ex OR

0

0

0

1

0

1

0

1

0

0

1

1

0

1

0

1

0

1

1

0

1

1

1

1

0

1

0

0



Digital circuit tips

-

guidance and hints and tips on using digital logic circuits


Digital logic circuits are widely used in today's' electronics. These circuits are
used for a very
wide variety of applications. From simple logic circuits consisting of a few logic gates, through to
complicated microprocessor based systems.


Whatever the form of digital logic circuit, there are a number of precautions that should be
obs
erved when designing, and also when undertaking the circuit board layout. If the circuit is
correctly designed and constructed then problems in the performance can be avoided.


Decoupling

One of the main points to ensure is that the power rails are adequat
ely decoupled. As the logic
circuits switch very fast, switching spikes appear on the rails and these can in turn appear on the
outputs of other circuits. In turn this can cause other circuits to "fire" when they would not
normally be intended to do so.


T
o prevent this happening all chips should be decoupled. In the first instance there should be a
large capacitor at the input to the board, and then each chip should be individually decoupled
using a smaller capacitor. The value of the capacitor will depend

upon the type of logic being
used. The speed and current consumption will govern the size of capacitor required, but typically
a 22nF may be used. For chips running with very low values of current a smaller capacitor may
be acceptable, but be aware that e
ven low current logic families tend to switch very fast these
days and this can place large voltage spikes onto the rails.


Some manufacturing companies suggest in their codes of practice that a proportion of the chips
should be decoupled. While this may b
e perfectly acceptable, the safest route is to decouple each
chip.


Earthing

The ground lines in a logic circuit of great importance. By providing an effective ground line,
problems such as ringing, spikes and noise can be reduced. In many printed circuit
boards a
ground plane is used. This may be the second side of a double sided board, or in some cases an
internal layer in a multilayer board. By having a complete, or nearly complete layer in the board,
it is possible to take any decoupling or earth points

to the plane using the shortest possible leads.
This reduces the inductance and makes the connection more effective. With the sharp edges, and
the inherent high frequencies that are present, these techniques are important and can improve the
performance.
For the more simple circuits that may be made using pin and wire techniques, good
practi
c
e is still as important, if not more so. Earth loops should be avoided, and earth wires
should be as thick as reasonably possible. A little planning prior to construct
ing the circuit can
enable the leads to be kept as short as possible.


General layout

The layout of a digital logic board can have a significant affect on its performance. With edges of
waveforms being very fast, the frequencies that are contained within t
he waveforms are
particularly high. Accordingly leads must be kept as short as reasonably possible if the circuit is
to be able to perform correctly. Indeed many high end printed circuit board layout packages
contain software that simulates the effects of
the leads in the layout. These software packages can
be particularly helpful when board or system complexity dictates that lead lengths greater than
those that would normally be needed are required to enable the overall system to be reali
z
ed.
However for m
any instances this level of simulation is not required, and lead lengths can be kept
short.


Unused inputs

In many circuits using logic ICs, inputs may be left open. This can cause problems. Even though
they normally float high, i.e. go to the "1" state, i
t is wise not to leave them open. Ideally inputs
to gates should be taken to ground, or if they need a logical "1" at the input they should be taken
to the rail, preferably though a resistor.


In many designs, spare gates may be available on the board. The

input gates to these circuits
should not be left floating as they have been known to switch and cause additional spikes on the
rails, etc. It is best practice to take the inputs of these gates to ground. In this way any possibility
of them switching in a
spurious manner will be removed.