DC Circuits

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7 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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LABORATORY ELECTRONICS II
DC Circuits •Basic DC circuits consist of resistors and batteries.
•Ohm’s law governs the behavior of resistors.
•Ohmic devices have a linear voltage - current relationship.
VIR=
VR
I
V
I
I
1
R
---
V
=
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LABORATORY ELECTRONICS II
Kirchhoff’s Laws •There are two rules that can be applied to circuit analysis.
•Kirchhoff’s current rule
•Kirchhoff’s voltage rule
I1
I3
I2
Current is conserved
I
3
I
1
I
2
+=
V1
V2
V3
V
1
V
2
V
3
++0=
Voltage is conserved
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LABORATORY ELECTRONICS II
Branch Method
•Label a current through each branch of
the circuit.
•Set up a set of independent equations
for the junctions (current law) and
loops (voltage law) in the circuit.
•Current law:
•Voltage law:
•Solve for I1, substituting for I3 and I2:
•Finally,
I1 = 3 mA, I2 = -1 mA, I3 = 2 mA.
V1
R1
I1
I2
I3
V2
R2
R3
V
1 = 16 V
V
2 = 6 V
R
1 = 2 kΩ
R
2 = 4 kΩ
R
3 = 5 kΩ
I
3
I
1
I
2
+=
V1
V
2
–R
1I
1
R
2I
2
–=
V
2
R
2I
2
R
3I
3
+=
V
2
R
2I
2
R
3I
1
R3
I
2
++=
V2
R
1
I
1
V
2
V1
–R3
I
1
R
3
R2
⁄()R1
I1
V2
V1
–+()+++=
R1
R2
I1
R2
R3
I1
R1
R
3
I
1
++R
2
V
1
R
3
V
1
R
3
V
2
–+=
I1
R2
V1
R
3
V
1
R
3
V
2
–+()=R
1R
2
R2
R3
R1
R3
++()⁄
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LABORATORY ELECTRONICS II
Load Line
V-I Curves •A battery and resistor in series has a characteristic voltage - current graph.
V
R
I
V
I
V
V=V0-IR
I
1
R
---
V0
V–()
=
V0
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LABORATORY ELECTRONICS II
Thevenin Equivalent
•Any circuit of batteries and resistors can be reduced to one battery and one resistor in series.
•Any set of circuit equations is reduced to V(I) = Vth − IRth.
Procedure 1.Find the voltage with no external circuit as Vth.
2.Find the current that would flow through an external short circuit.
3.Find the equivalent resistance as Rth
= Vth/Isc.
4.The Rth
is the same if all batteries are shorted and resistance measured.
Norton’s Theorem •Any circuit of batteries and resistors can be reduced to one current source and one resistor in
parallel.
V
th
R
th
I
V
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LABORATORY ELECTRONICS II
4-Terminal Circuits •Voltage dividers
•The ratio V
out/V
in is the gain A.
•V
out
= f(V
in) is the transfer characteristic.
Z1
Z2
Vin
V
out
Vout
Vin
----------
Z
2
Z1
Z
2
+
------------------
=
Z1
Z2
Vin
V
out
V
in
V
out
A
Z2
Z1
Z2
+
------------------
=
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LABORATORY ELECTRONICS II
Diodes
•Diodes permit one-way current flow.
•Diode behavior displayed as a v-i characteristic
V
A
V
B
If V
in > V
out
+ 0.6 V, i > 0

I
If V
in < V
out
+ 0.6 V, i = 0

I
V
A - VB
II
S
e
VΔVT

1–()
=
VD
0.6V≅
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LABORATORY ELECTRONICS II
Bipolar Junction Transistor •The BJT is built like a diode sandwich.
•Quantum properties of the BJT allow for transconductance.
•The emitter follower has the emitter voltage track the base voltage.
B
C
E
C
E
B
npnpnp
IC
βI
B
=
V
CC
R
E
vout
vin
VE
VB
0.6V–=
vout
v
in
=
IE
I
C
I
B
+β1+()I
B
==
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LABORATORY ELECTRONICS II
Field Effect Transistor •MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor) has an input (gate) impedance
which is very high (10
14 Ω).
•The MOSFET can be used as a
bidirectional switch, like a
mechanical switch.
•There is a voltage divider with RDS
and the 47 kΩ resistor.
•When the gate is ground or
negative, RDS > 1010 Ω, vout
<
0.0001vin.
•When the gate is + 15 V, RDS = 100
Ω, vout = 0.998 vin.
G
D
S
S
D
G
n-channelp-channel
BB
vin
Vcontrol
vout
100 kΩ
47 kΩ
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LABORATORY ELECTRONICS II
Operational Amplifiers
•An op-amp is a difference amplifier with power supplies at V+ and V
-.
•Op amps have special properties when used with negative feedback.
•There are two rules to analyze a circuit with an op amp.
1.I+ = I- = 0
2.v+ - v- = 0
A0
v+
vout
V
+
v−
V−
1
2
3
45
6
7
8
V−
v−
v+
V+
vou
t
vout
= A0(v1 - v2)
V
in
V
out
+

R1
R2
v+
v-
I2
I1
A
V
out
Vin
-----------
I1
R
1
I2
R
2
+
I1
R
1
-----------------------------
1
R2
R1
------
+===
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LABORATORY ELECTRONICS II
Forward Bias Diode
•Consider a single diode with an AC signal.
•A diode will “short-circuit” signals in the forward direction.
•Real diodes are modeled by an equivalent resistance and diode voltage drop.
RL
vin
+

vout
RL
vf
vout
RL
vf
vout
VD
r
f
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LABORATORY ELECTRONICS II
Reverse Bias
•A diode will block signals in the reverse direction.
•Real diodes pass a small amount of reverse current.
RL
vr
vout
RL
vr
vout
ID
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LABORATORY ELECTRONICS II
Half-wave Rectifier
•Ideal behavior doesn’t match real behavior.

•Forward voltage is slightly less.
•Reverse current isn’t zero.
V0
Forward
vout
V0
Reverse
vin
V0-VD
Forward
vout
V0
Reverse
vin
-I0RL
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LABORATORY ELECTRONICS II
Full-wave Rectifier
•Two half-have rectifiers in parallel make a
full-wave rectifier.
•When vin is positive the current flows
through P
1, RL, and P2.
•When vin is negative the current flows
through N1, RL, and N2.
RL
vin
+

vout
P
1
N2
N1
P2
V0-2VD
vout
V0
v
in
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LABORATORY ELECTRONICS II
Diode Clamp
•A clamps cuts off current at voltages other than ground.
If vin > 5.6 V, vout
= 5.6 V.
•Two diodes reversed in parallel become a limiter.
If vin > 0.6 V, vout
= 0.6 V, if vin < - 0.6 V, vout
= - 0.6 V
1 kΩ
vin
vout
+ 5 V
RL
vin
vout
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LABORATORY ELECTRONICS II
Zener Diode
•Zener diodes have well defined reverse breakdown voltages and allow sufficient current to flow to
maintain a constant voltage drop.
If vin > VZ, vout
= VZ.
•Two zeners can be combined to form a
limiter.
If vin > VZ + Vf, v
out
= VZ, if vin < -(VZ + Vf),
vout
= -(VZ + Vf)
•The pair of diodes are sold in one package
as a transient suppressor.
RL
vin
vout
VZ
RL
vin
vout
VZ
RL
vin
vout
VZ
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LABORATORY ELECTRONICS II
Diode Bias
•Diodes can bias a circuit to a value other than 0 volts.
•Without the diode this is a high-pass filter.
•With the diode: for vin = V0 sin ωt , vout
= vin + V0 − 0.6 V.
D
C
vin
vout
iD
R
V0 - 0.6 V
Forward
vout
V0
Reverse
vin