electrical engineering EE80T HW 5

HOMEWORK #5 (only use this if PDF doesn't work, PDF has models) 

1) Radar:

While traveling in your car, you are caught going above the speed limit by a cop with a radar gun.

Suppose his radar gun sent out a signal at 24GHz and the radar gun's frequency mixer outputs a

difference frequency of 6.72kHz. This is a much more realistic set of frequencies than those used in

lecture.

a) What frequency was picked up by the receiver?

b) The speed (v) of an object causing a doppler frequency shift of ?f is v=(?f/f)*(c/2), f is the original

frequency and c is the speed of light. How fast were you driving in mph and m/s?

c) What frequency would you observe if you pointed it at an asteroid approaching the planet at 1% of

the speed of light? Probably the last measurement you would ever make?

2) Low-pass filter:

We must build a filter to separate the difference frequency in problem 1 (6.72kHz), from the sum

frequency, which is much higher. A good cutoff for this low-pass would be 20kHz. In the following low

pass circuit, Vs=10V and R=150?. This is typical of a real design problem in which engineers design

circuits to meet a particular specification and then check the performance of their design.

a) What capacitor value would give us our desired cutoff frequency, where ?=1/(RC)?

b) Graph the impedance vs frequency of the capacitor at f=200Hz, 2kHz, 20kHz, 200kHz, and 2MHz.

You can use the log-log graph paper on the last page of this file.

c) On the other sheet of graph paper, plot Vo/Vin of this circuit at the same five frequencies. Note that

now that we know the impedance of the capacitor, we can treat the circuit as a voltage divider.

d) How much smaller than the desired signal is the signal that you are trying to get rid of at this filter?s

output?

3) Resonant Circuit:

Figure out how the voltage divides across Rs and this equivalent impedance to determine how much

voltage appears at the output.

The values of the components above are as follow: Vs= 1mV, Rs=100 ?, C=1 nF, L=2.5x10-5 H, and

Ro=1 M?.

a. What is the resonant frequency of just the L and C combination? At this frequency the parallel

combination of just the ideal L and C is infinite.

b. Fill in the following table for the requested values for each of the different source frequencies.

Frequency

100 kHz

1 MHz

10 MHz

Magnitude

of the

impedance

of C

Magnitude

of the

impedance

of L

Approximate

Equivalent

impedance

of C, L, & Ro Vout

To find the approximate magnitude of the equivalent impedance recall that for impedances in parallel

the impedance will be roughly equal to the smallest impedance if the others are all much bigger (just

like for resistors). This is approximate because technically you can?t just use the parallel impedance

formula if you have both inductors and capacitors at the same time. For instance, actually at resonance

the equivalent impedance of the L and C in parallel is infinite (use this fact above, but we won?t prove

it?). Note at which frequency the output voltage is largest.

c) Finally at 100 kHz and 10 MHz across which component does most of the source voltage appear?

4) Radio Tuning:

When you tune your radio, you might not be aware that what you?re actually modifying in the radio

circuitry is the frequency of a ?local oscillator?. Both the local oscillator and incoming radio stations

are the inputs to the mixer, whose output (you might recall from lecture) are the sum and difference

frequencies. Consider the Super-heterodyne receiver below.

a. Suppose you want to listen to your favorite sports radio AM station,

KNBR on 680 AM. Assuming the IF stage is tuned to 455 kHz when you tune to

KNBR on your AM radio, to what frequency did you actually set the local oscillator?

b. At this frequency of the local oscillator, what is the other frequency that

appears at the output of the mixer?

c. Whom do we have to thank for the Super-heterodyne circuit

5) Diode:

Consider the circuit shown below. The input signal is a 100Hz square wave with a Vp-p = 2 V the

voltage is changing symmetrically around zero volts. What is the shape of the output waveform?

Assume that the diode is ideal with zero resistance when it is conducting. For full credit, you must

VOUT

a) Draw the input waveform, clearly state what the axes represent and plot your waveform to scale.

b) Draw the output waveform.

c) Draw the waveform of the voltage across the diode

d) How would the output voltage waveform change if you reversed the diode? Make a sketch of this

new waveform

Reading Questions:

6) What frequency range can humans hear? What is the frequency of the ?lowest growl? of a pipe

organ?

7) (T/F) Philo T. Farnsworth received the first patent for a TV system which he called the ?electric

telescope?.

8) Who got the idea for the gun-director and how did this idea come to this person?