Download Homework 15

ECE 252 Introduction to Electrical Engineering
Lesson 15. Frequency Response, Filters, and Resonance Homework
Version S17
Homework partner name: _______________________Homework partner name: ________________________
1. Quickies
a) The gain of an RC filter (either hi-pass or lo-pass) at the cutoff frequency is _________________ .
b) If an RC filter has an output of 7 V at its half-power point, the output voltage will be _______________ V at
the cutoff frequency.
c) If a device has a gain of 90, its gain in dB is ___________________ dB.
d) If a device has a gain of -10.3 dB, its gain (not in dB) is ___________________.
e) Two devices are in series. The first has a gain of 12 and the second has a gain of 0.5. The net gain is _______.
f) An amplifier with a gain of 15 has an input voltage of 50 mV. Its output is ________________ mV.
g) Two devices are in series. One has a gain of 18 dB and the other has a gain -5 dB. The net gain is ______ dB.
h) A low-pass filter has R = 25 kΩ and C = 0.3 µF. The input to the filter is connected to a circuit with a
Thevenin equivalent voltage of 7 mV and a Thevenin equivalent resistance of 18 kΩ. The cutoff frequency of the
combined devices is ________________ Hz.
Signatures: ________________________________________________________________________
2. (a) Design a low-pass filter with a cutoff frequency of 3400 Hz. Use a 0.2 µF capacitor and an appropriate
resistor (calculate its value). (b) Sketch and label the circuit. (c) What is the gain of the filter at the cutoff
frequency? Give your answer both as a ratio (Vout/Vin) and in dB. (d) What is the gain of the filter at a frequency
of 2500 Hz? Give your answer both as a ratio (Vout/Vin) and in dB.
(a)
(b)
(c)
(d)
Signatures: ________________________________________________________________________
3. A high-pass filter is shown below. C = 2 pF. R = 800 kΩ. (a) What is its cutoff frequency? The output of this
filter is connected to an amplifier with an input resistance of 300 kΩ. (b) Sketch and label the new circuit. (c)
What is the new cutoff frequency?
(a)
(b)
(c)
Signatures: ________________________________________________________________________
4. (a) Design a band-pass filter consisting of an RC high-pass filter with a cutoff frequency of 500 Hz feeding an
RC low-pass filter with a cutoff frequency of 900 Hz. Carefully select the R and C of each filter so that one filter
does not load the other, changing the cutoff frequencies. Make one of the two resistors equal to 1 kΩ. (b) Sketch
and label the circuit. (c) Calculate the gain of the band-pass filter at 500 Hz, 700 Hz, and 1100 Hz.
(a)
(b)
(c)
G500 =
G700 =
G1100 =
Signatures: ________________________________________________________________________
5. A series-resonant RLC circuit has R = 200 Ω, L = 12 mh, and C = 20 pF. (a) Sketch and label the circuit. (b)
Find fo, the resonant frequency. (c) At what frequency is impedance a minimum? (d) What is the magnitude of the
impedance at this frequency?
(a)
(b)
(c)
(d)
6. A parallel-resonant RLC circuit has R = 250 Ω, L = 4 mh, and C = 550 pF. (a) Sketch and label the circuit. (b)
Find fo, the resonant frequency. (c) At what frequency is impedance a maximum? (d) What is the magnitude of
the impedance at this frequency? (e) What is the magnitude of the impedance at infinite frequency?
(a)
(b)
(c)
(d)
(e)
Signatures: ________________________________________________________________________
BONUS (No partial credit.) Ten high-pass RC filters are connected together. Each has a cutoff frequency of 1000
Hz. Assuming the filters can be treated independently (i.e. they don’t load each other), what is the gain in dB of
this filter combination at a frequency of 2000 Hz?
Signatures: ________________________________________________________________________