ECE 2A Lab #7
Lab 7
AC Circuits and
Transformers
Overview
In this lab we introduce the impedance concept in the context of simple voltage divider/filter
circuits. You will also experiment with a simple audio-transformer.
Table of Contents
Pre-lab Preparation
Before Coming to the Lab
Required Equipment
Parts List
In-Lab Procedure
7.1
The Impedance Concept
A Reactive Voltage Divider
Second-Order Low-Pass Filter
7.2
Transformers
Turns Ratio: Voltage Transformation
Impedance Transformation
2
2
2
2
3
3
3
3
4
5
6
1
© Bob York
2
AC Circuits and Transformers
Pre-lab Preparation
Before Coming to the Lab
□
Read through the details of the lab experiment to familiarize yourself with the
components and testing sequence.
□
One person from each lab group should obtain a parts kit from the ECE Shop.
Required Equipment
■ Provided in lab: Bench power supply, Function Generator, Oscilloscope, Decade Box
■ Student equipment: Solderless breadboard, and jumper wire kit
Parts List
Qty
1
1
1
2
2
2
Description
10mH 19DCR power inductor (from Lab #6)
100uH power inductor
75mW audio transformer, 10k-ct primary, 2k-ct secondary
1uF 25V electrolytic c apacitor, radial lead
10uF 25V electrolytic capacitor, radial lead
100uF 25V electrolytic capacitor, radial lead
We will also use the 741 op-amps and selected components from earlier labs
© Bob York
In-Lab Procedure
3
In-Lab Procedure
7.1 The Impedance Concept
A Reactive Voltage Divider
Vout
The circuit in Figure 7-1 is a basic AC voltage V
in
Z
1
divider with a unity-gain buffer amplifier at
+
the input. By using an input buffer amp we
Z2
can subsequently assume that the voltage
divider will be driven by a nearly ideal voltage
source; this is useful because the bench
function generator has a potentially significant Figure 7-1 – Voltage divider with input buffer.
output impedance (you may recall that you
saw the effect of this in one of the first-order filter circuits in the previous lab). Thus if we
eliminated the input buffer stage we’d have to add the output resistance of the function
generator in series with Z1 in all our calculations.
The AC response of the voltage divider will depend on the impedances that we use for Z1
and Z 2 . For example, if we use two capacitors the transfer function would become
1
Vout
Z2
jC2
C1



(7.1)
1
1
Vin Z1  Z 2
C1  C2

jC1
jC2
A result that is independent of frequency. So a capacitive voltage divider behaves in some
respects like a resistive voltage divider, although the dependence on the series and shunt
values is reversed.
□
Build the circuit shown in Figure 7-1 using two 1μF capacitors. As always with op-amp
circuits, start by adding the power-connections first, then add the remaining components.
Keep the power off until you are ready to make measurements.
□
Using your cables, connect the function generator as Vin, and set up your oscilloscope to
observe Vin and Vout simultaneously as in the previous lab. Adjust the function
generator to produce a 0.1V amplitude sinewave at 1kHz.
□
Turn on the power and record the output voltage, and compare with the theoretical
prediction in (7.1). Adjust the frequency a little around 1kHz to convince yourself that
the output is frequency-independent.
Despite the similarities to a resistive divider there is one significant difference here: the
current supplied by the buffer amplifier is now strongly dependent on frequency! The net
impedance between the op-amp output and ground is Z1  Z 2 . At high-frequencies the
capacitor has a very small impedance, and this may excessively load the op-amp.
Second-Order Low-Pass Filter
Now let Z1  R1  j L1 and Z 2  1 / jC2 ; the transfer function in this case is
Vout
Z2
1 / jC2
1



2
Vin Z1  Z 2 R1  j L1  1 / jC2 (1   L1C2 )  j R1C2
(7.2)
4
AC Circuits and Transformers
The behavior of this circuit can be appreciate by looking at limiting values of frequency. As
  0 the transfer function approaches a constant value of one (1). As    the transfer
function diminishes in proportion to 1 /  2 . Thus we anticipate a low-pass character to the
response. But notice that something interesting happens when  2 L1C2  1 ; at this frequency
the transfer function becomes
  0 
1
L1C2

Vout
1
1 L1


0 R1C2 R1 C2
Vin
(7.3)
This point is called the resonant frequency of the circuit, and for small values of resistance
R1 the transfer function could be greater than one at resonance. In other words, there is
effectively a kind of voltage gain in the
circuit due to the interaction of the
L1
Vout
inductor and capacitor. Note that R1
V
in
could represent the parasitic winding
+
resistance of the inductor; it does not have
C2
to be a separate component:
□
Turn off power and rebuild the circuit
as shown in Figure 7-2 using
Figure 7-2 – Second-order low-pass.
L1  10 mH and C2  1  F . Adjust
the amplitude of the function generator to a 10mV amplitude sinewave.
□
Turn on power and adjust the frequency to the vicinity of the resonant frequency
f 0  0 / 2 . Use (7.3) to estimate the resonant frequency. Vary the frequency around
this point to see if there is a frequency at which the output voltage peaks. If so, record
this frequency and the peak voltage.
□
Now take data necessary to generate a “Bode plot” later on (a Bode plot is just a log-log
plot of the transfer function versus frequency). Start at around 50Hz and stop at around
20 kHz (e.g. 50Hz, 100Hz, 200Hz, 500Hz, 1kHz, 2kHz, etc.). You may need to use a
smaller step in the vicinity of the resonance.
Now turn off power and rebuild the circuit using L1  100  H and C2  100  F . Then
repeat the last two steps for this new configuration.
Use MATLAB or Excel to generate a nice log-log plot of the frequency response of this
second-order low-pass filter in your lab report.
□
7.2 Transformers
N1 : N2
We now switch gears a bit to introduce
the transformer.
A transformer is
essentially two inductors that share a
common magnetic flux. This is usually
accomplished by winding them around a
common magnetic “core” of iron,
Bend tabs up before
ferrite, or other material of highinserting into breadboard
magnetic permeability.
The transformer used in this lab is a
Figure 7-3 – Audio transformer with center-taps.
small “audio” transformer.
This is
designed to operate at low power levels in the 100Hz-20kHz range. A drawing and
schematic of the audio transformer is shown in Figure 7-3. In this particular case each
© Bob York
5
Transformers
winding has a center-tap, or an extra terminal attached to the middle of each winding. Not all
transformers have center tapped windings; we’ll see how they can be used momentarily (and
also in ECE 2B).
□
As a first step, insert the audio transformer into your breadboard across one of the IC
channels, just as you would with an op-amp (leave the previous op-amp/filter circuit
intact and insert the transformer in a separate region of the breadboard). You will need to
first bend tabs back on transformer as shown in Figure 7-3. You can do this using your
needle-nose pliers. Be careful when you insert the transformer, the wires are thin so they
can sometimes just crimp instead of descending into the holes. Straighten out the wires
first and line them up with the holes, then use your pliers to gently press the wires into
place one at a time.
Turns Ratio: Voltage Transformation
In general each winding on the transformer has a different number of turns. One winding is
called the primary, the other is called the secondary. Its often hard to know which is the
primary and secondary without measurements, but the
N1 : N2
transformer in this lab has two markings to help: one
side of the windings has a “P” marked on it for
Vin
“primary”, and looking down at the top, one side of
the bobbin is colored black.
Vout
Consult the data sheet for the actual turns ratio for
your transformer; if it’s the one we expect, the
primary should have N1  2100 turns and a 500 Ω
DC resistance, and the secondary should have Figure 7-4 – Basic test set-up for
N 2  600 turns and a 200 Ω DC resistance.
examining the open-circuit voltage
□
Adjust the function generator for a 0.1V transformation.
amplitude sinewave at 1kHz and apply to the
primary leads as shown in Figure 7-4. Please note that the primary and secondary share a
common ground! Monitor the input and output voltages across the two windings using
the oscilloscope. Record the waveforms and peak values in your notebook. Ideally the
ratio of output voltage to input voltage should scale with the turns ratio as
Vout N 2
(7.4)

Vin
N1
Now switch things around: apply the input signal to the secondary and monitor the output
across the primary. What changes? Again record the waveforms and peak values, can
compare the results of these last two steps with the ideal (7.4).
In real transformers the magnetic properties of the
N2 : N1
iron or ferrite core material are influenced by the
amount of current in the windings, so the actual
voltage transformation ratio will depend to some
Vin
extent on the amplitude of the input signal and any
Vout
loading currents in later parts of the lab. Thus our
experiments may not match (7.4) perfectly.
□
□
Now apply the input signal to the center-tap on
the secondary and record the output across the
primary as shown in Figure 7-5. Compare the
Figure 7-5 – Using the center-taps.
6
AC Circuits and Transformers
result with the previous step. Can you see what is happening? Applying the signal to the
center tap only uses half of the turns in the winding, so the ratio of output signal to input
signal should be doubled.
□
Rebuild the circuit now with the input signal
applied across the full secondary winding
and the output recorded across half of the
primary as shown in Figure 7-6. Now we
are only using half the turns at the output, so
the voltage ratio should be reduced by half
compared with your earlier data. Record
your findings.
N2 : N1
Vin
Vout
Figure 7-6 – More fun with center-taps!
Impedance Transformation
A transformer is a passive device, so the output power must always be less than the input
power. Thus if the transformer is used to step UP the voltage, the current must go down
proportionally. If the power dissipated in the device is minimal then we can expect the
current to transform exactly in the opposite way as the voltage:
I out N1
(7.5)

I in
N2
The fact that current and voltage scale
in opposite ways leads to an interesting
and useful application of transformers
as an impedance transformer. We will
demonstrate this using resistors as
shown in Figure 7-7. In this case, using
(7.4) and (7.5) we can easily show that
R1
Iin
N1 : N2
Iout
Vg
Vin
Vout
RL
2
N 
V
Rin  in   1  RL
I in  N 2 
(7.6)
If N1  N 2 , we can use this trick to
make a small resistance look bigger to
the rest of the circuit.
Rin
Figure 7-7 – Circuit for demonstrating the impedancetransforming property of transformers.
Configure the circuit in Figure 7-7 on your breadboard using R1  10 k and RL  1 k .
Apply a 1kHz @ 0.1V amplitude sinewave for Vg and observe Vg and Vin on the
oscilloscope. Record the amplitude of Vin and compare with your expectation based on
your knowledge of voltage dividers and the prediction of (7.6)
Real transformers are not easy to model accurately. In addition to the winding resistances
and winding inductances, there are parasitic capacitances between the turns on each winding,
and as mentioned previously the nonlinear properties of the core requires some effort to
characterize properly. We have basically ignored these complications in our treatment above,
so it shouldn’t be too surprising if there are some departures from the theoretical predictions.
□
Congratulations!
You have now completed Lab 7
© Bob York