EKT 214
Tutorial 5 : Active Filters
Solutions
Basic Filter Response
1) State 4 basic categories of active filters.
- Low Pass Filter
- High Pass Filter
- Band Pass Filter
- Band Stop Filter
2) Sketch and label between the actual and ideal response curve of the 4 categories
of active filters
LPF:
HPF:
NMN
April 2011
Page 1
EKT 214
BPF:
BSF:
3) What determines the bandwidth of a low-pass filter?
- Critical frequency because critical frequency determines the passband.
4) Explain how the selectivity is affected by the Q of a filter.
- Q and BW are inversely related. The higher the Q, the better the selectivity
and vice versa.
5) A single-pole high-pass filter has a frequency-selective circuit with R=2.5 kΩ and
C=0.0018 µF. Determine the critical frequency, fc and roll-off rate of the filter
described.
-
fc 
1
2 RC
- fc = 1/ (2π(2.5k)(0.0018µ)) = ____________
- role off rate = -20dB/ decade
NMN
April 2011
Page 2
EKT 214
Filter Response Characteristics
6) What is the center frequency of a filter with a Q of 20 and a bandwidth of 2 kHz.
- Q = fc / BW
- fc = 20(2k) = 40kHz
7) State the characteristics of Butterworth, Chebyshev and Bessel response.
- Butterworth is very flat in passband and has a -20db/decade/pole roll-off.
Chebyshev has ripples in the passband and has greater than 20db/decade/pole roll-off. Bessel has a linear phase characteristic and less
than -20db/decade/pole roll-off.
8) Name the basic parts of active filters.
- Frequency selective circuit
- Gain element
- Negative feedback circuit
Active Low-Pass Filters
9) How many poles does a second-order low pass-filter have? How many resistors
and capacitors are used in the frequency-selective circuit?
- A second order filter has 2 poles. Two resistors and two capacitors make up
the frequency selective circuit.
10) Design active low-pass filters with the following roll-off rates by using singlepole and two-pole low pass filters with Butterworth responses.
i)
NMN
April 2011
-40dB/decade
Page 3
EKT 214
ii)
-60dB/decade
Active High-Pass Filters
11) How does a high-pass Sallen-Key filter differ from the low-pass configuration?
- The positions of Rs and Cs in the frequency-selective circuit are opposite
for low-pass and high-pass configurations.
12) If three two-pole high-pass filters and one single-pole high-pass filter are
cascaded, what is the resulting roll-off?
= -140dB/decade
Active Band-Pass Filters
13) One filter has a Q = 5 and another has a Q = 25. Which has the narrower
bandwidth?
- Q = 25. Higher Q gives narrower BW.
14) Design a multiple-feedback band-pass filter with the maximum gain, Ao = 8,
quality factor, Q = 25 and center frequency, fc =10 kHz. Assume that C1 = C2 =
0.01µF. Draw the circuit design of the active band-pass filter.
- R 
1
Q
2f o CAo
R2 
Q
f o C
R3 
Q
2f o C (2Q 2  Ao )
- R1 = _______ , R2 = _______ and R3 = _______
NMN
April 2011
Page 4
EKT 214
C1
R2
R1
C2
V in
V out
R3
15) Determine the center frequency, fc, quality factor, Q and bandwidth, BW for the
band-pass output of the state-variable filter in Figure 1. Given that R1 = R2 = R3 =
25 kΩ, R4 = R7 =2.5 kΩ, R5 = 150 kΩ, R6 = 2.0 kΩ, C1 = C2 = 0.003µF.
Figure 1
- For integrator, fc = 1/2πR4C1 or fc = 1/2πR7C 2
- The center frequency is approximately equal to critical frequency of integrators,
fo = fc = 1/2πR4C1 = _____________
-

1 R
Q   5  1
\ 3 R6


- Q = ________.
- BW = fo / Q = __________.
NMN
April 2011
Page 5
EKT 214
Active Band-Stop Filters
16) How does a band-stop response differ from a band-pass response?
- Band stop rejects frequencies within the stopband. A band pass passes frequencies
within the passband.
NMN
April 2011
Page 6