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