EECE 253 – Homework
Filters (Chapter 14 in text)
Problems:
1) Design a series RLC circuit that will have an impedance of R = 10 Ω at the resonant
frequency of ω0 = 50 rad/sec and a quality factor of 80. Find the bandwidth.
2) Design a parallel resonant RLC circuit with ω0 = 10 rad/sec and Q = 20. Calculate
the bandwidth of the circuit. Let R = 10 Ω.
3) A parallel resonance circuit has a resistance of 2 kΩ and half-power frequencies of
86 kHz and 90 kHz.
Determine:
a) the capacitance
b) the inductance
c) the resonant frequency
d) the bandwidth
e) the quality factor
4) Show that the circuit below is a lowpass filter. Calculate the corner frequency fc if
L = 2 mH and R = 10 kΩ .
5) Determine the cutoff frequency of the lowpass filter described by
H (ω ) =
4
2 + 10 jω
Find the gain in dB and the phase of H(ω) at ω = 2 rad/s.
6) Design an RL lowpass filter that uses a 40 mH coil and has a cutoff frequency of 5
kHz.
7) Design a series RLC type bandpass filter with cutoff frequencies of 10 kHz and 11
kHz. Assuming C = 10 pF, find R, L and Q.
8) Design an RC highpass filter that has a cutoff frequency of 2 kHz and uses a 300 pF
capacitor.
9) Determine the centre frequency and bandwidth of the bandpass filters below.
10) A highpass filter is shown below. Show that the transfer function is:
R f ⎞ jωRC
⎛
⎟⎟
H (ω ) = ⎜⎜1 +
R
i ⎠ 1 + jωRC
⎝
11) A “general” first-order filters is shown below.
a) Show that the transfer function is
⎛ R4 ⎞ s + (1 / R1C )(R1 / R2 − R3 / R4 )
⎟⎟
,
H ( s ) = ⎜⎜
s + 1 / R2C
⎝ R3 + R4 ⎠
s = jω
b) What condition must be satisfied for the circuit to operate as a highpass filter?
c) What condition must be satisfied for the circuit to operate as a lowpass filter?
12) Design an active lowpass filter with a dc gain of 0.25 and a corner frequency of 500
Hz.
13) Design an active highpass filter with a high-frequency gain of 5 and a corner
frequency of 200 Hz.