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ELEC 350L
Electronics I Laboratory
Fall 2003
Lab 3: T-Bridge Amplifier and D/A Converter
Introduction
Op-amps are versatile electronic devices and are employed in a wide range of applications in
both analog and digital circuitry. One important application is high-gain analog amplification.
The use of negative feedback makes possible the design of stable high-gain amplifiers, which is a
difficult task with other electronic amplifying devices. Even so, care must be taken to limit the
sensitivity of the feedback network to environmental conditions. The T-bridge amplifier circuit
was developed to address this requirement. Another important application of op-amps is digitalto-analog (D/A) conversion. A good D/A converter can be built using a summing amplifier
based on an op-amp. A convenient characteristic of this type of circuit is that the voltage gains
from the various input ports to the output port are set simply by adjusting resistor ratios. This
simplifies the tasks of controlling the conversion process and of scaling the output voltage. In
this lab experiment you will build a high-gain amplifier with a T-bridge feedback network and a
D/A converter based on the summing amplifier circuit.
Theory of Operation
a. Inverting Amplifier with T-Bridge Feedback Network
To achieve high gain in a standard op-amp inverting amplifier, the feedback resistor must have a
very large value, especially if the input resistance (set by the resistor connected to the inverting
input of the op-amp) has to be relatively large. The use of large resistors to control gain can pose
a problem if there is stray resistance or capacitance in parallel with the feedback resistor. Such
stray impedances can lower the effective impedance of the feedback path. This problem can be
avoided by employing a “T” network that uses resistors with smaller values. An inverting
amplifier with a T-bridge feedback network is shown in Figure 1 on the next page.
The circuit is easily analyzed (as are most op-amp circuits) using nodal analysis. At the
inverting input of the op-amp, application of Kirchhoff’s Current Law (KCL) yields
Vin 0  Va

,
R1
R2
which simplifies to
Va  
R2
Vin .
R1
Note that a virtual short is assumed to exist across the op-amp’s input terminals, which dictates
that the node voltage at the inverting input must be 0 V. At the node marked Va, KCL leads to
0  Va Va Vo  Va


 0,
R2
RB
RA
which becomes
1
R

R
Vo   A  A  1Va .
 R2 RB 
R2
va
RA
RB
R1
+15 V
_
v in
vo
+
-15 V
Figure 1. Inverting amplifier with T-bridge feedback network.
Substitution of the equation for Va into the equation for Vo yields directly the expression for the
voltage gain of the amplifier,
R
R
R
Vo   A  A  1 2 Vin .
 R2 RB
 R1
Comparison of this gain formula to that for the simple inverting amplifier,
Vo  
R2
Vin ,
R1
illustrates that substantially higher gain can be achieved using smaller resistor values with the
T-bridge circuit than with the standard circuit.
b. D/A Converter using a Summing Amplifier
Digital-to-analog converters are widely used in many modern communications and
instrumentation systems. This type of circuit is the heart of all musical compact disk playback
units. The basic function of the D/A converter is to translate (convert) a number represented in
binary form to an analog voltage value that corresponds to that number. For example, a 3-bit
D/A converter might be designed to produce the output voltages shown in Table 1 for the eight
possible binary numbers that can be represented by three binary digits.
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Table 1. Output of a 3-bit D/A converter for all possible inputs.
Binary
Output
Number Voltage (V)
000
0.0
001
0.2
010
0.4
011
0.6
100
0.8
101
1.0
110
1.2
111
1.4
Although the output voltages shown in Table 1 range from zero to 1.4 V, a D/A converter can be
designed to provide any desired range of output voltages. Most D/A converters are designed to
have equal-sized increments (steps) from one voltage level to the next. In the example shown in
Table 1, the step size is 0.2 V. If smaller step sizes are desired for a given output voltage range
(that is, if greater resolution is needed), then a larger number of bits must be used to represent the
voltage values.
A 3-bit D/A converter can be built easily using a summing amplifier based on an op-amp. A
typical circuit is shown below in Figure 2.
R2
v2
Rf
R1
v1
R0
+15 V
_
v0
v out
+
-15 V
Figure 2. 3-bit D/A converter based on a summing amplifier.
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It is easy to show that the output voltage of the summing amplifier is given by
vout  
Rf
R0
v0 
Rf
R1
v1 
Rf
R2
v2 .
Note that the subscript on v0 is a zero, not to be confused with the letter “O,” which is often used
to indicate output. In the D/A converter circuit the input voltages are interpreted as representing
the three bits of a binary number. A binary 0 is usually represented by 0 V, and a binary 1 is
usually represented by some particular nonzero (typically positive) voltage value. Input voltage
v0 represents the least significant bit (LSB), v1 the second bit, and v2 the most significant bit
(MSB). The input resistors R0 through R2 must be chosen so that a change in state in the bit
applied to a given input causes an appropriate corresponding change in the output voltage. For
example, for a converter circuit designed to produce the outputs given in Table 1, if v0 changes
from 0 to 1, the output voltage must change by 0.2 V. Likewise, if v1 changes from 0 to 1, the
output voltage must change by 0.4 V; and if v2 changes, the output must change by 0.8 V. (Note
that the voltage increments are related to each other by powers of 2.) These requirements dictate
that R0 must be twice the value of R1 and that R1 must be twice the value of R2. The value of Rf
sets the overall output voltage range obtained for the full range of input binary numbers between
000 and 111.
There is one other important issue to consider when using a summing amplifier as a D/A
converter. The binary digit 1 is usually represented in digital circuits by a positive voltage value
(+5 V is commonly used). However, if positive voltages are applied to the inputs of the
summing amplifier, the resulting output voltage will be negative. Often this is not a problem, but
if it is, an inverting amplifier with a gain of –1 can be added to the output of the summer to
create a positive output voltage.
Experimental Procedure
a. Inverting Amplifier with T-Bridge Feedback Network
Assemble a standard inverting amplifier circuit like the one investigated in Lab #2. Design the
amplifier to have a gain of –60 ( 5%) and an input resistance of 150 k ( 5%). Use power
supply voltages of ±15 V. Use nearest standard values for all required resistor values. Apply a
sinusoidal voltage at a frequency of approximately 1 kHz to the input of the op-amp. Note that
you will have to use a small-amplitude input signal to avoid the presence of clipping in the
output voltage waveform. (You may need to use a voltage divider like the one you investigated
in Lab #1.) Once you have the circuit operating, touch the two ends of the feedback resistor with
two fingers from one hand and note any effects it has on the output voltage. What do you think
is causing the effects you see? Next place your fingers across the input resistor. Do you see any
effects? Why or why not?
Now design and build the T-bridge circuit shown in Figure 1 to have a gain as close as possible
to –60 and an input resistance of 150 k. Again, use power supply voltages of ±15 V, and apply
the same small-amplitude sinusoidal input signal at a frequency of around 1 kHz. Once again
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place two fingers from one hand across the feedback network. Do you see any of the same
effects you observed with the standard inverting amplifier? Are they more or less severe (or the
same) than with the simple amplifier? How would you explain the differences (if any) that you
observe? Again place your fingers across the input resistor. Do you see any effects this time?
Why or why not?
b. D/A Converter using a Summing Amplifier
Design a 3-bit D/A converter using the summer circuit shown in Figure 2. Set the 0-6 V section
of the bench-top power supply to 5 V. Use this voltage to represent the binary digit 1, and use
0 V (ground) to represent the binary digit 0. Use values roughly in the 10 k to 100 k range
for the input resistors R0 through R2. Choose the value of the feedback resistor Rf of the
summing amplifier so that the binary number 111 produces an output voltage of –3.5 V, and add
a simple inverting amplifier with a gain of –3 (using reasonable values for the resistors) to the
output of the summing amplifier. The output voltage increment will therefore be 1.5 V with
eight output voltage values ranging from 0 to +10.5 V. Note that, since you must use standard
values for all of the resistors in your circuit, you may not be able to create the exact resistor
ratios that you want. Try to get as close as possible to your design values, but don’t spend too
much time working out a solution. After all, the resistors available in the lab don’t have very
tight tolerances. Also, remember that you can always combine resistors in series and/or parallel
to obtain non-standard values, but for practical reasons you should limit such combinations to no
more than two resistors.
Create a truth table like the one shown in Table 1 for your circuit by measuring the actual output
voltages obtained for the various input combinations. Create a logical 0 state at an input by
connecting that input to ground, and create a logical 1 by connecting the input to the 0-6 V
power supply (adjusted to +5 V). Measure the output voltage using the bench-top voltmeter
instead of the oscilloscope. Using a voltmeter will allow you to measure voltages to at least
three digits of accuracy. Do you obtain the intended output voltage values for each input state?
Why or why not?
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