–
Recall that we used this idea earlier to calculate the DC voltage at
the output.
•
At high frequencies (F large), V
out
= V
in

23
M. Horowitz, J. Plummer, R. Howe
Frequency Dependence of RC Circuit
v
in
v
out
R
C
F
V
out
/V
in
FRC
j
FRC
j
V
V
in
out
p
p
2
*
1
2
*
+
=
•
This circuit passes high frequencies but
blocks low frequencies.
•
Sometimes called a “high pass filter”.

24
M. Horowitz, J. Plummer, R. Howe
Analyzing RC Circuits Using Impedance
(High Pass Filter)
v
in
v
out
C=0.1
μ
F
FRC
j
FRC
j
FC
j
R
R
V
V
in
out
p
p
p
2
*
1
2
*
2
*
1
+
=
+
=
RC = 11ms; 2
p
RC about 70ms
0
0.2
0.4
0.6
0.8
1
0
50
100
150
200
V
out
/V
in
F (Hz)
R=11 k
W

25
M. Horowitz, J. Plummer, R. Howe
Impedance of Other RC Circuits
Series : Z
eq
=
Z
1
+
Z
2
=
R
1
+
R
2
R
1
R
2
R
1
R
2
C
2
C
1
C
2
C
1
Parallel: Z
eq
=
1
1
Z
1
+
1
Z
2
=
R
1
R
2
R
1
+
R
2
Series : Z
eq
=
Z
1
+
Z
2
=
1
j
∗
2
π
FC
1
+
1
j
∗
2
π
FC
2
=
1
j
∗
2
π
F
1
C
1
+
1
C
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
=
1
j
∗
2
π
F
C
1
C
2
C
1
+
C
2
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
Parallel: Z
eq
=
1
1
Z
1
+
1
Z
2
=
1
j
∗
2
π
FC
1
+
j
∗
2
π
FC
1
=
1
j
∗
2
π
F C
1
+
C
2
(
)

26
M. Horowitz, J. Plummer, R. Howe
Impedance of Other RC Circuits
Series : Z
eq
=
Z
1
+
Z
2
=
R
+
1
j
∗
2
π
FC
=
1
+
j
∗
2
π
FRC
j
∗
2
π
FC
R
R
C
C
Parallel: Z
eq
=
1
1
Z
1
+
1
Z
2
=
1
1
R
+
j
∗
2
π
FC
=
R
1
+
j
∗
2
π
FRC
Check limits on these expressions!

27
M. Horowitz, J. Plummer, R. Howe
Learning Objectives for Today
•
Generalize RC circuit analysis in the time domain
•
Impedance is the relationship between voltage and current
–
For a sinusoidal input
–
Z = V/I so for a capacitor, Z = 1/2πFC or 1/j*2πFC
•
Understand how to use impedance to analyze RC circuits
–
Compute the “voltage divider” ratio to find output voltage
–
Calculate series and parallel effective impedances

#### You've reached the end of your free preview.

Want to read all 27 pages?

- Spring '20
- Inductor, RC circuit, Electrical impedance