2 class days
Lab 4: Diode Circuits
Lab Assignment
1. LRC Resonant Circuit
Eyler lab 3 modified (HH 3.1)
Construct a parallel RLC filter using the following setup (HH Lab 3-1, with
modified component values.) Drive the circuit with a sine wave, varying the
frequency through a range that includes the circuit’s resonance (which should be
somewhere between about 3 KHz and 100 KHz depending on the value of L).
Some of the inductors are difficult to insert in the breadboards, so be patient and
try not to force them.
To scope,
10X probe
Recommended
.
Use 2 mH < L < 50
mH
Find the resonant frequency ω0. Measure the amplitude of VLC as a function of
frequency, taking enough points to make a respectable plot. For an elegant
display, try using the frequency sweep option available on the function generator;
see the notes from Lab 2 in Hayes and Horowitz. Measure the series resistance
RL of the inductor with an ohmmeter; you will need this to answer the questions
below. Finally, try using this filter to find the Fourier components of a square
wave as suggested on pp. 75-76 of Hayes and Horowitz.
Plot the response of the parallel RLC resonant circuit. What is the Q factor (the
ratio of the resonant frequency to the full width at the 3 dB points)? Can you
account for the measured value of Q by using the values of the resistor R and the
measured series resistance RL of the inductor, or are additional loss mechanisms
playing a role?
2. Half-wave Rectifier
HH 3.2. Answer all questions.
3. Full-wave Bridge Rectifier
HH 3.3. Answer all questions.
4. Ripple Current
HH 3.4. Answer all questions. Compare the size of your observed ripples with
your calculation. Why does your calculation predict a larger ripple than
observed? Please note you should be using a polarized capacitor in this lab.
5. Diode Mixer
Source: Eyler lab 4
Construct a basic mixer circuit as shown below, omitting the capacitor initially.
The two signal generators are connected through 1K resistors so their outputs do
not perturb one other. Despite this precaution, some signal generators do not
perform acceptably, so make substitutions if necessary. The 510 Ω resistor is
used to provide a bias voltage, so the diode is always slightly conducting even
when no input signal is present. A direct connection can’t be used because the
signals would then be shorted to the power supply, which has very low ac
impedance. The 4.3K resistor is used both to limit the bias current and to sample
the current through the diode.
Set the two signal generators to produce sine waves with nearly identical
frequencies somewhere near 100 KHz. Using an oscilloscope with 10´ probe,
look at the top (anode) of the diode and set the amplitudes so that each signal
generator substantially perturbs the dc level, but without actually reverse-biasing
the diode (why?) Now look at the output voltage across the 4.3 K resistor (at the
cathode of the diode). You should see a modulated envelope, something like
this:
Try varying the frequency of either signal generator to change the difference
frequency. What happens if the amplitudes are too large?
Next, connect a capacitor across the 4.3 K resistor to form a low-pass filter, so
you can see the difference frequency without the high-frequency oscillations.
Choose the capacitance so that RC is slow compared to the 100 KHz inputs, but
fast compared to the difference frequency (10 KHz, say). You may want to use
ac coupling on the oscilloscope, so you can see the small signal without the dc
level set by the bias current. Experiment until you get a clean sinusoidal
difference frequency output.
Once things are working well, you can explore for some of the other difference
frequencies produced by the diode. You should be able to see a weak output
whenever the two frequencies are nearly rational multiples of one another, like
3:2, 2:1, and so forth.
Verify the discussion above by explicitly writing the response of the diode as a
sum of sinusoids, finding the constants in the expression below. (Hint: it’s
probably easiest to write things using complex notation, then regroup the terms)
I = c1 (V12 + V2 2 ) + c2 (V1 cos !1t + V2 cos !2 t )
+ c3 (V1V2 cos(!1 " !2 )t + c4 (V1V2 cos(!1 + !2 )t + c5 (V12 cos 2!1t + V2 2 cos 2!2 t )
+ terms in higher orders of V1 , V2 .
Why is the bias voltage needed to obtain satisfactory operation without severe
distortion?
When you connect the filter capacitor the response is diminished noticeably,
even if the difference frequency is much lower than the RC time constant. Why
does this happen?
6. Effects of instruments on your readings
Source: HH 3.8
Part D – Input Impedance of Scope
HH 3.8, from “Now use a similar trick to measure the input resistance of the
scope.” through “Try it!”.
Part E – Internal Resistance of Function Generator
HH 3.8, very last paragraph.