Problem 9. A three-pole filter a) For a simple 1 pole series-R, shunt-C filter you want a pole at wp = 2π-100 MHz. Choose values that meet this requirement and while ensuring |Zin > 5 KQ for all frequencies. R= C= Value
Problem 9. A three-pole filter a) For a simple 1 pole series-R, shunt-C filter you want a pole at wp = 2π-100 MHz. Choose values that meet this requirement and while ensuring |Zin > 5 KQ for all frequencies. R= C= Value
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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![Problem 9. A three-pole filter
a) For a simple 1 pole series-R, shunt-C filter you want a pole at wp = 2π-100 MHz.
Choose values that meet this requirement and while ensuring |Zin > 5 KQ for all
frequencies.
R=
C=
Value
b) Consider the Sallen Key filter shown, which can provide complex conjugate (c.c.) poles.
V₁
R₂
R₁ V₂
HH
J
RE
out
Derive its transfer function, as well as Vout/V1 and V₁/Vin and confirm the following
relationships:
DC gain: Avo = (RF/RA+1)
Natural frequency of c.c. poles: wn = (R₁R₂C1C2) ¹1/2
Quality factor of c.c. poles: Q = [wn(R1C1 + R2C1 + R2C2(1 - Avo)]-1
[Hint] 1) First find the DC gain (capacitors = open), 2) find the gain from V₁ to Vout, 3) use
the miller effect (and noting that C2 is in positive feedback) to estimate the impedance
presented to node V₁ by R₁ and C2, and 4) find V₁/Vin, and Vout/Vin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe71fa9fe-4c50-495d-8e14-2d45567e8c37%2F5be7dd8c-738e-47ac-9b84-7377ca904f47%2F4lu794ya_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 9. A three-pole filter
a) For a simple 1 pole series-R, shunt-C filter you want a pole at wp = 2π-100 MHz.
Choose values that meet this requirement and while ensuring |Zin > 5 KQ for all
frequencies.
R=
C=
Value
b) Consider the Sallen Key filter shown, which can provide complex conjugate (c.c.) poles.
V₁
R₂
R₁ V₂
HH
J
RE
out
Derive its transfer function, as well as Vout/V1 and V₁/Vin and confirm the following
relationships:
DC gain: Avo = (RF/RA+1)
Natural frequency of c.c. poles: wn = (R₁R₂C1C2) ¹1/2
Quality factor of c.c. poles: Q = [wn(R1C1 + R2C1 + R2C2(1 - Avo)]-1
[Hint] 1) First find the DC gain (capacitors = open), 2) find the gain from V₁ to Vout, 3) use
the miller effect (and noting that C2 is in positive feedback) to estimate the impedance
presented to node V₁ by R₁ and C2, and 4) find V₁/Vin, and Vout/Vin.
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