CP2 Circuit Theory Revision lecture

piquantdistractedElectronics - Devices

Oct 5, 2013 (3 years and 11 months ago)

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CP2 Circuit Theory

Revision Lecture

Basics,
Kirchoff’s

laws,
Thevenin

and Norton’s
theorem, Capacitors, Inductors


June 2004 q7


September 2010 q7


AC
theory, complex notation, LCR circuits


September 2005 q8


June 2002 q7


Op
-
amps

Sam Henry (Tony Weidberg
) www.physics.ox.ac.uk/users/weidberg/teaching

V
0

I

R
1

R
2

R
3

V
0

IR
1

IR
2

IR
3
=0

+

+

+

+










V
0

+IR
1

+IR
2

+IR
1

I
1

I
3

I
2

I
4

I
1
+I
2

I
3

I
4
=0

Kirchoff’s laws

V
eq

R
eq

R
eq



Thevenin

and Norton theorem

In Practice, to find V
eq
, R
eq


R
L


(open circuit) I
L

0 V
eq
=V
L

R
L

0 (short circuit) V
L

0

R
eq
= resistance between terminals
when all voltages sources shorted


Capacitors

C

+Q

-
Q

Q = CV

Capacitors resist change in voltage


Capacitors in series



Capacitors in parallel



Stored energy



stored in form of electric field

C
1

C
2

C
N


Inductors





Inductors in series



Inductors in parallel



Stored energy




stored in form of magnetic field

L

“back
emf”

Self
-
inductance

Inductors resist a
change of current

L
1

L
2

+

V
0

R

+

V
0

R

L

C

RC and RL circuits

CP2 June 2004

Check


Energy conservation:


Total energy dissipated
by resistor = Energy
delivered by source

CP2 September 2010

AC circuit theory


Voltage represented by complex exponential




Impedance relates current and voltage V=ZI

in complex notation:



Resistance


R


Inductance


j

L


Capacitance

1/j

C


and combinations thereof


Impedance has magnitude and phase

represented by real component of

easily shown from


Q=VC


Current is given by






So |Z| gives the ratio of magnitudes of V and I, and


give the
phase difference by which current lags voltage

CP2 September 2005

The complex impedance is given by the voltage in a circuit
divided by the current when both are expressed in complex
form. The magnitude of the complex impedance is the ratio
of the magnitudes of the voltage and current; the phase is
the phase lag between the voltage and current.

Physics 3 June 2002

An oscillating voltage of frequency
ω
, V(t)=V
0
cos(
ω
t) is represented
in complex notation by V
0
e
j
ω
t
. The current in the circuit is then given
by I=V/Z, where Z is the complex impedance Z=|Z|
e
j
φ
, where |Z| is
the ratio of the magnitude of the voltage to the magnitude of the
current, and
φ

is the phase by which the current leads the voltage.
The real component of Z is the resistance, and the imaginary
component is the reactance






where C the capacitance and
L is the inductance of the circuit. Complex impedances allow circuits
when inductance and capacitance to be analysed using linear circuit
theory in the same way as resistance




The sum of these peak voltages
is not equal to V
0

as V
R
, V
C

and
V
L
all have different phases.
When the complex voltages are
summed V
R
+V
C
+V
L
=V
0

LCR circuit

overdamped solution

critically damped solution

underdamped (oscillatory) solution

+

V
0

R

C

L

I(t)

Op
-
amps

Gain is very large (A

)

Inputs draw no current (Z
IN
=

)

Feedback


v
+
=v


V
OUT

+



v
+

v


V
IN

R
1

R
2

Non
-
Inverting
Amplifier Circuit

+

V
OUT

V
IN

R
1

Inverting Amplifier Circuit

R
2



v


v
+

i

i