For the circuit shown in Figure P7.12, the parameters are R 1 = 10 kΩ , R 2 = 10 kΩ , R 3 = 40 kΩ , and C = 10 μF . (a) What is the value of the voltage transfer function V o / V i at very low frequencies? (b) Determine the value of the voltage transfer function at very high frequencies. (c) Derive the expression for the voltage transfer function T ( s ) = V o ( s ) / V i ( s ) . Put the expression in the form T ( s ) = K ( 1 + s τ A ) / ( 1 + s τ B ) . What are the values of K , τ A , and τ B ? Figure P7.12
For the circuit shown in Figure P7.12, the parameters are R 1 = 10 kΩ , R 2 = 10 kΩ , R 3 = 40 kΩ , and C = 10 μF . (a) What is the value of the voltage transfer function V o / V i at very low frequencies? (b) Determine the value of the voltage transfer function at very high frequencies. (c) Derive the expression for the voltage transfer function T ( s ) = V o ( s ) / V i ( s ) . Put the expression in the form T ( s ) = K ( 1 + s τ A ) / ( 1 + s τ B ) . What are the values of K , τ A , and τ B ? Figure P7.12
Solution Summary: The author explains the value of voltage transfer function at low frequency.
For the circuit shown in Figure P7.12, the parameters are
R
1
=
10
kΩ
,
R
2
=
10
kΩ
,
R
3
=
40
kΩ
, and
C
=
10
μF
. (a) What is the value of the voltage transfer function
V
o
/
V
i
at very low frequencies? (b) Determine the value of the voltage transfer function at very high frequencies. (c) Derive the expression for the voltage transfer function
T
(
s
)
=
V
o
(
s
)
/
V
i
(
s
)
. Put the expression in the form
T
(
s
)
=
K
(
1
+
s
τ
A
)
/
(
1
+
s
τ
B
)
. What are the values of K,
τ
A
, and
τ
B
?
This is a practice question from my Introduction to Circuits course.
I am having a hard time finding the poles for this. When I implement the circuit in LT Spice, I can see that the cutoff frequency is somewhere around 16kHz, but I can't figure out how to come up with that value mathematically. It is underdamped; so, will have imaginary components, but I'm lost as to how to find them or what to do with them or how to come up with the correct cutoff frequency to match LT Spice.
Thank you for your assistance.
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