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Sallen–Key topology - Quiz
Contributed by: Appleby
  • 1. Where are the poles of the Sallen-Key topology transfer function located?
A) s=α±√(α2−ω02)
B) s=−α±√(α2+ω02)
C) s=α±α2+ω02
D) s=−α±α2−ω02
  • 2. How many zeros at infinity does the Sallen-Key topology transfer function have?
A) Three
B) Zero
C) Two
D) One
  • 3. What is the Q value for a second-order Butterworth filter in Sallen-Key topology?
A) √2
B) 1
C) 2
D) 1/2
  • 4. Which of the following expressions represents the relationship between Q, m, and n in Sallen-Key topology?
A) Q=mnm2+1
B) Q=mn/(m2+n2)
C) Q=mn+m+n
D) Q=(m+n)/(mn)
  • 5. What is the expression for ω0 in terms of R and C?
A) ω0=R/C
B) ω0=1/RC
C) ω0=RC
D) ω0=C/R
  • 6. In the context of Sallen-Key topology, what does setting C1 as nC and C2 as C/n achieve?
A) It fixes the ratio between resistors.
B) It eliminates the poles in the transfer function.
C) It increases the circuit's noise production.
D) It reduces the expressions for f0 and Q.
  • 7. What is a consequence of choosing high resistor values in Sallen-Key topology?
A) Reduced need for precise component matching.
B) Improved frequency response.
C) Decreased circuit's noise production.
D) Increased circuit's noise production and DC offset voltage on op amp outputs.
  • 8. For a second-order unity-gain Sallen-Key low-pass filter, what is the input impedance given by?
A) Z(s)=R1s2+s/Q+1s2+sk/Q
B) Z(s)=R1s'2+s′/Q+1s'2+s′k/Q
C) Z(s)=R1s'+s'/Q+1s'+sk/Q
D) Z(s)=R1s'2+Q/s′+1s'2+k/s′
  • 9. What is the condition for Q to have a minimal value of the magnitude of impedance in Sallen-Key topology?
A) Q<1−k22
B) Q>1−k22
C) Q≠1−k22
D) Q=1−k22
  • 10. What is the approximate expression for |Z(s)|min in Sallen-Key topology?
A) |Z(s)|min=R1(1+Q2)/k2+0.34
B) |Z(s)|min=R11Q+k2+0.5
C) |Z(s)|min≈R11Q2+k2+0.34
D) |Z(s)|min=R1/Q+k2+0.34
  • 11. For which range of k values is the approximation for |Z(s)|min considered accurate?
A) 0.5≤k≤1.0
B) 0.7≤k≤1.0
C) 0.25≤k≤0.75
D) 0.1≤k≤0.3
  • 12. What is the approximate expression for ωmin in Sallen-Key topology?
A) ωmin=ω0/Q2+Q4+k2(2Q2+k2−1)
B) ωmin≈ω02Q22Q2+k2−1
C) ωmin=ω0(Q2+Q4)/(k2+1)
D) ωmin=ω02/(Q2+k2)
  • 13. In which year was the Sallen-Key topology introduced?
A) 1955
B) 1965
C) 1985
D) 1975
  • 14. What type of amplifier is typically used in a Sallen-Key filter?
A) Inverting amplifier
B) Voltage follower with high gain
C) Differential amplifier
D) Unity gain amplifier
  • 15. The Sallen-Key topology is a degenerate form of which type of filter?
A) LC filter
B) Digital IIR filter
C) VCVS filter
D) Passive RC filter
  • 16. What is a key advantage of cascading VCVS filters?
A) Stages do not affect each other's tuning
B) They reduce overall filter order
C) Increase the number of poles
D) Require fewer resistors
  • 17. What type of components are avoided in VCVS filters?
A) Diodes
B) Resistors
C) Inductors
D) Capacitors
  • 18. In the Sallen-Key topology, what is connected to the op amp's inverting input?
A) To ground
B) Through a capacitor only
C) Directly to the output (vout)
D) Through an inductor
  • 19. What law is applied at the vx node for analyzing Sallen-Key topology?
A) Kirchhoff's current law (KCL)
B) Ohm's Law
C) Faraday's Law
D) Ampere's Law
  • 20. What is the typical response of a second-order LTI system in Sallen-Key filters?
A) Non-linear time-invariant system
B) First-order linear time-variant system
C) Second-order linear time-invariant (LTI) system
D) Third-order non-linear system
  • 21. What component is used to bootstrap the 'bottom' of Z3 in a Sallen-Key filter?
A) Operational amplifier with high gain
B) Buffer amplifier
C) Voltage divider
D) Resistor network
  • 22. What is a common alternative to an operational amplifier in modern Sallen-Key filters?
A) Emitter or source followers
B) Diode rectifiers
C) Transformer coupling
D) Transistor amplifiers
  • 23. What is the primary reason for using a unity gain amplifier in Sallen-Key filters?
A) To amplify signal frequency
B) To implement a buffer amplifier
C) To increase output voltage
D) To decrease input impedance
  • 24. What is the role of Kirchhoff's current law in analyzing Sallen-Key topology?
A) Determines filter order
B) Applied at the vx node to derive equations
C) Used to determine power consumption
D) Helps in calculating component tolerances
  • 25. What is the typical configuration for Z3 in a Sallen-Key topology?
A) Disconnected entirely
B) Connected to ground
C) Connected to vout
D) Connected through an inductor
  • 26. Which component is frequency-dependent in terms of impedance?
A) Inductor
B) Resistor
C) Capacitor
D) Diode
  • 27. In a Sallen-Key low-pass filter, what are Z1 and Z2 typically set to?
A) Z1 = C1, Z2 = C2
B) Z1 = 1/sC1, Z2 = 1/sC2
C) Z1 = R1, Z2 = R2
D) Z1 = L1, Z2 = L2
  • 28. What type of filter topology is discussed in the text?
A) Chebyshev
B) Elliptic
C) Sallen–Key
D) Butterworth
  • 29. In the context of a high-pass filter, what does 'ζ' represent?
A) Resonance frequency
B) Damping factor
C) Quality factor
D) Gain
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