Test 9.1 Resonance

The resonant frequency ω of a passive circuit is the frequency at which

the output voltage is a maximum.
the output current is a maximum.
the input impedance is purely real.
the input impedance is purely imaginary.

Test 9.2 dB Scale

Convert the power ratio to dB: P_out/P_in = (120)^1/4.

10.4 dB
2.6 dB
-5.2 dB
5.2 dB

Test 9.3 dB Scale

Convert the voltage ratio to dB: V_out/V_in = (120)^1/4.

10.4 dB
2.6 dB
-5.2 dB
5.2 dB

Test 9.4 Bode Plot

Which expression corresponds to this Bode plot?

H(ω) = 10ω(1 + jω)
H(ω) = 20ω/(1 + jω)
H(ω) = 10ω/(1 + jω)
H(ω) = 20ω(0.1 + jω)

Test 9.5 Bode Plot

Which expression corresponds to this Bode plot?

H(ω) = 1000(1 + jω/5)/(1 + jω/50)
H(ω) = 10⁶(1 + jω/5)²/(1 + jω/50)²
H(ω) = 1000(1 + jω/50)³/(1 + jω/5)³
H(ω) = 10⁶(1 + jω/5)³/(1 + jω/50)³

Test 9.6 Frequency Limits

At dc,

V_o/V_i = 0.33
V_o/V_i = 0
V_o/V_i = 1
V_o/V_i = 0.25

Test 9.7 Frequency Limits

As ω → ∞,

V_o/V_i = 0.33
V_o/V_i = 0
V_o/V_i = 1
V_o/V_i = 0.25

Test 9.8 Active Filter

Given the following values for the components in the given circuit:
R_s1 = 10 kΩ
R_s2 = 100 kΩ
R_f1 = 100 kΩ
R_f2 = 100 kΩ
C_f1 = 4 × 10^-9 F
C_s2 = 8 × 10^-9 F
For this bandpass filter, the corner frequencies of its lowpass and highpass stages are

ω_LP = 2.5 krad/s and ω_HP = 1.25 krad/s
ω_LP = 1.25 krad/s and ω_HP = 2.5 krad/s
ω_LP = 12.5 krad/s and ω_HP = 25 krad/s
ω_LP = 25 krad/s and ω_HP = 12.5 krad/s

Test 9.9 Series RLC Circuit

The fractional bandwidth (B/ω₀) of this bandpass filter is

B/ω₀ = 2
B/ω₀ = 4
B/ω₀ = 0.2
B/ω₀ = 0.1

Test 9.10 Series RLC Circuit

The quality factor of this bandpass filter is

Q = 10
Q = 5
Q = 2
Q = 1

Test 9.11 Parallel RLC Circuit

The quality factor of this bandpass filter circuit is

Q = 0.2
Q = 1
Q = 2
Q = 5

Test 9.12 Series RLC Circuit

What kind of filter is this?

Highpass
Lowpass
Bandpass
Bandreject

Test 9.13 Roll-Off Rate

Generally speaking, the roll-off rate for a second-order lowpass circuit is

10 dB/decade
20 dB/decade
40 dB/decade
60 dB/decade

Test 9.14 Bode Plot

Which is the correct expression for the Bode plot?

H(ω) = 10(1 + jω/10)(1 + jω/10⁴)/[(1 + jω/100)(1 + jω/1000)]
H(ω) = 100(1 + jω/10)(1 + jω/10⁴)/[(1 + jω/100)(1 + jω/1000)]
H(ω) = 100(1 + jω/100)(1 + jω/1000)/[(1 + jω/10)(1 + jω/10⁴)]
H(ω) = 10(1 + jω/100)(1 + jω/1000)/[(1 + jω/10)(1 + jω/10⁴)]

Test 9.15 Resonance

At resonance,

V_out/V_in = 0.8
V_out/V_in = 0.4
V_out/V_in = 0.2
V_out/V_in = 0.1

Test 9.16 Frequency Limits

In the limits as ω→0 and ω→∞,

V_out/V_in → -1 as ω→0, and V_out/V_in → 1 as ω→∞
V_out/V_in → 1 as ω→0, and V_out/V_in → 1 as ω→∞
V_out/V_in → 0 as ω→0, and V_out/V_in → 1 as ω→∞
V_out/V_in → 1 as ω→0, and V_out/V_in → 0 as ω→∞