Frequency Response

In a two-terminal electrical network containing at least one inductor and one capacitor, what is the definition of resonance?

What is the formula for the resonant frequency, ω₀, of a parallel RLC circuit?

A parallel resonant circuit is composed of an 8 kOhm resistor, a 50 mH inductor, and an 80 nF capacitor. What is the resonant frequency, ω₀, for this circuit?

What is the quality factor, Q, of a resonant circuit defined as?

For a parallel RLC circuit, what is the expression for the quality factor at resonance, Q₀?

A parallel RLC circuit has L = 2 mH, C = 10 nF, and a quality factor Q₀ = 5. What is the value of the resistor R?

What is the relationship between the exponential damping coefficient α and the resonant frequency ω₀ and quality factor Q₀ for a parallel RLC circuit?

The half-power frequencies, ω₁ and ω₂, are defined as the frequencies where the magnitude of the input admittance of a parallel resonant circuit is greater than its magnitude at resonance by what factor?

What is the formula for the bandwidth, B, of a resonant circuit in terms of its resonant frequency ω₀ and quality factor Q₀?

For a high-Q circuit where Q₀ is greater than or equal to 5, the upper and lower half-power frequencies, ω₁ and ω₂, can be approximated by what expression?

A parallel resonant circuit has a resonant frequency f₀ = 440 Hz and Q₀ = 6. Using the approximate expressions for a high-Q circuit, what are the estimated lower and upper half-power frequencies, f₁ and f₂?

By the principle of duality, what is the quality factor Q₀ for a series RLC circuit?

A series resonant circuit is composed of a 10 Ohm resistor, a 200 nF capacitor, and a 2 mH inductor. What is the quality factor, Q₀, of this circuit?

What is the primary difference in impedance characteristics at resonance between a series RLC circuit and a parallel RLC circuit?

Magnitude scaling is defined as the process by which the impedance of a two-terminal network is increased by a factor of Km. How must L and C be scaled to achieve this?

Frequency scaling is defined as the process by which the frequency at which any impedance occurs is increased by a factor of Kf. How must L and C be scaled to achieve this?

A parallel resonant circuit has R = 2.5 Ohm, L = 0.5 H, and C = 2 F. It is to be scaled to have a new resonant frequency of 5 x 10^6 rad/s and a new impedance maximum of 5000 Ohm. What are the new component values R', L', and C'?

The value of a transfer function's magnitude |H(jω)| in decibels (dB) is defined by which formula?

A transfer function magnitude |H(jω)| increases by a factor of 10. How much does its value in decibels (HdB) increase?

In a Bode magnitude plot, what is the slope of the high-frequency asymptote for a simple zero, H(s) = 1 + s/a?

For a simple zero H(s) = 1 + s/a, what is the difference between the exact magnitude and the asymptotic magnitude at the corner frequency ω = a?

What are the three straight-line segments that form the asymptotic phase response for a simple zero H(s) = 1 + s/a?

What is the Bode magnitude plot for the transfer function H(s) = 1 / (1 + s/a)?

For the transfer function H(s) = -2s / [(1 + s/10)(1 + s/20,000)], what is the asymptotic magnitude in dB in the flat region between ω = 10 rad/s and ω = 20,000 rad/s?

What is the slope of the high-frequency asymptote for a transfer function with a quadratic zero, H(s) = 1 + 2ζ(s/ω₀) + (s/ω₀)²?

For a quadratic factor H(s) = 1 + 2ζ(s/ω₀) + (s/ω₀)², what is the correction needed at the corner frequency ω = ω₀ when the damping factor ζ = 0.5?

Which type of filter passes frequencies below a cutoff frequency and significantly attenuates frequencies above it?

The transfer function for a simple passive RC low-pass filter (output across the capacitor) is H(s) = Vout/Vin = 1 / (1 + RCs). Where is the corner frequency located?

To design a simple passive RC high-pass filter with a corner frequency of 3 kHz, a 4.7 kOhm resistor is chosen. What is the required capacitance?

A simple RLC series circuit is used as a bandpass filter with the output taken across the resistor. The bandwidth B of this filter is given by what expression?

An active low-pass filter is to be designed with a cutoff frequency of 10 kHz and a DC voltage gain of 40 dB. The design uses a noninverting amplifier. What is the required ratio of Rf/R1 for the amplifier?

What is a primary advantage of using active filters (e.g., with op-amps) over passive filters?

The low-pass Butterworth filter is known for what characteristic in its passband?

In a Sallen-Key low-pass filter prototype with R1 = R2 = R and C1 = C2 = C, what is the required amplifier gain G for a second-order Butterworth response?

To design a third-order Butterworth filter, what factors must the transfer function denominator contain?

What does a damping factor ζ > 1 imply for a quadratic factor H(s) = 1 + 2ζ(s/ω₀) + (s/ω₀)²?

For a series combination of a 100 mH inductor and a 5 Ohm resistor, what is the parallel equivalent resistance, Rp, at a frequency of 1000 rad/s, using the high-Q approximation?

A network is scaled in frequency by a factor of Kf = 2. If the original impedance was found at a frequency ω, at what frequency will the same impedance value be found in the new network?

At resonance in a simple parallel RLC circuit, what is the net current flowing into the parallel LC combination?

A circuit's frequency response is measured in decades. What does one decade represent?

What is the key feature of a Chebyshev filter's passband response compared to a Butterworth filter?

In the context of the Bode plot for H(s) = 1 + s/a, the frequency 'a' is often described as the corner, break, or half-power frequency. What other name is it given?

A series RLC circuit has a resonant frequency of 50 krad/s and Q₀ = 10. A voltage of 100 mV is applied. What is the approximate current magnitude if the operating frequency is 48 krad/s?

The input impedance of a network is Z(s) = 2 + 5s. How would its magnitude vary as a function of frequency ω, when σ=0?

What type of filter is created by taking the output across the resistor in a series RLC circuit?

To convert a series combination of a resistance Rs and a reactance Xs to a parallel equivalent (Rp, Xp), which statement about their quality factors (Q) must be true?

What is the slope of the Bode phase plot for a transfer function H(s) = s?

A circuit with a transfer function H(s) is scaled in magnitude by Km = 10 and in frequency by Kf = 100. If the original transfer function was Z(s), what is the new transfer function Z''(s)?

What is the primary trade-off in choosing a Chebyshev filter over a Butterworth filter of the same order?

A transfer function has a magnitude of 0.5. What is its value in decibels (dB)?