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Do you have a square waveform generator, but not a real pulse generator for testing the integrator? Here is a
simple (crude) way to get the pulse you need -- about 1 millisecond long, 1-5 volts high, 50 pulses each second.
It generates a more-or-less square pulse on every rising edge of the input square wave. Adjust . . .
--the repetition rate by the waveform generator's frequency (50 Hz)
--the width of the output pulse by the waveform generator's amplitude (low)
--the amplitude of the output pulse using the 10K pot
0.1 F
1N914
741 op-amp
INTEGRATOR
+
SQUARE WAVE IN
10K
1N914
10K
pot
10K
input
impedance
Believe me when I tell you that this turkey will not be found in any book of standard circuits; it's a "make do with what
you've got" sort of kludge. A TTL one-shot (e.g. 74123) is a better way to go if you've got one. A waveform generator
chip is even better.
The first capacitor and resistor differentiate the square wave, producing short up-going and down-going pulses. The
first diode removes the down-going pulses. The op-amp, highly saturated, is usually at -15 V but rushes to +15 V
when the incoming pulse shows up. The 10K pot voltage divides the output to get a reasonable (and adjustable) pulse
height. The final diode keeps only the positive portion of the output pulse.
1
Here is a better pulse generator based on the 74LS123 dual one-shot (only one one-shot is used). The input is a square wave,
about 3 volts peak-to-peak, at the desired pulse repetition rate (e.g. 10-40 Hz). The outgoing pulse width is variable between
about 0.1 ms and 3.5 ms, and the outgoing pulse height is variable from 0 volts to about 3 volts -- plenty of variation to give the
voltage integrator a good workout.
not connected
pulse width
adjustment
14 C
EXT
0.1F
15 RC
+5V
EXT
connected
74LS123
100K
~3 V peak-to-peak
~40 Hz
16 V
10K
2B
CC
IN
1N914
QOUT 13
amplitude
adjustment
Integrator
10K
10K
1A
IN
8 GND
The 74LS123 is powered by +5 volts (pin 16) and ground (pin 8). Do not connect +15 V or -15 V to this chip!
Set the two pots to about midrange and the input waveform generator to low amplitude. Power up. Increase the
waveform generator's amplitude until you see output pulses, but don't go beyond about 4 volts peak-to-peak on the
input. Adjust the two pots to get the output pulse width and amplitude that you need to exercise the voltage integrator.
2
The Leaky Voltage Integrator
The upper trace is the incoming pulse to be integrated. Its amplitude is very small.
The lower trace is the output of the integrator. You can see it growing (downward) during the input pulse, and discharging
(leaking) during the long wait until the next input pulse.
Two questions:
1. Is the leak so large that it has a significant impact on the accuracy of the integration? Remember that the leaking
doesn't stop during the input pulse.
2. Is the integrator's capacitor adequately discharged before the next pulse arrives?
VOUT
3
Calculating the Basic Properties of the Inverting Amplifier
Since no current flows in or out of the op-amp input terminals, the current I through R1 must be the same as the current through R2. I = V/R for
both resistors. Hence
[1] (VOUT - VIN-) / R2 = (VIN- - VSRC) / R1 Multiplying by R1R2 . . .
[2] R1 (VOUT - VIN-) = R2 (VIN- - VSRC) Expanding . . .
[3] R1 VOUT - R1 VIN- = R2 VIN- - R2 VSRC
[4] By definition, the open-loop gain of the op-amp is GOL = -VOUT / VIN- (with VIN+ at ground) so VIN- = -VOUT / GOL . Substituting for VIN- in [3] . . .
[5] R1 VOUT + R1 VOUT / GOL = -R2 VOUT / GOL - R2 VSRC Multiplying by GOL and collecting terms with VOUT . . .
[6] R1 GOL VOUT + R1 VOUT + R2 VOUT = -R2 VSRC GOL
[7] VOUT = -VSRC R2 GOL / (R1 GOL + R1 + R2) which for very large GOL becomes just VOUT = -VSRC (R2 / R1).
In the general case, the two equations in red, [7] then [4], will yield V OUT and VIN- given VSRC , GOL , R1 and R2 .
[8] It is useful to define the actual gain of the entire circuit G CIRC = -VOUT / VSRC = R2 GOL / (R1 GOL + R1 + R2) (from [7]) Inverting . . .
[9] 1 / GCIRC = (R1 GOL + R1 + R2) / R2 GOL = R1 / R2 + R1 / R2 GOL + 1 / GOL
[10] We can define the ideal (very large GOL) gain of the amplifier as GIDEAL = R2/R1. Multiplying [9] by GIDEAL . . .
[11] GIDEAL / GCIRC = 1 + 1 / GOL + GIDEAL / GOL = (GOL + GIDEAL + 1) / GOL .
[12] GCIRC = GIDEAL  GOL / (GOL + GIDEAL + 1)
In words, the actual gain of the amplifier is the ideal gain R 2/R1 multiplied by a correction factor that is nearly 1 for op-amps with very large openloop gains but becomes significantly less than 1 as the op-amp gain becomes comparable to the ideal gain.
Clearly you can reach the troublesome region where the correction factor is significantly less than 1 by (1) operating the op-amp in a frequency
regime where its open-loop gain is low, or (2) demanding that the gain of your amplifier be very high, or (3) even worse, both.
4
What is the effect on a feedback-controlled inverting amplifier if the op-amp does not have a very high open-loop gain? Let's
consider the inverting amplifier (circuit #1).
R1 -- the input resistor (e.g. 10 K)
R2 -- the feedback resistor (e.g. 100 K)
VSRC -- the voltage at the input to the circuit (referenced to ground)
VIN- -- the voltage at the inverting input of the op-amp (referenced to ground since VIN+ is at ground)
VOUT -- the voltage at the op-amp (hence circuit) output (referenced to ground)
GOL -- the open-loop gain of the op-amp  -VOUT / VIN- for VIN+ at ground
GCIRC -- actual circuit gain  -VOUT / VSRC for VSRC and VOUT referenced to ground
Noting that no current flows in or out of the VIN- terminal, we can compute the current through R1 and R2:
I = (VOUT - VSRC) / (R1 + R2) and the voltage drop across R2: (VOUT - VIN-) = I  R2.
As defined above, VOUT = -GOL VIN- ; VIN- = -VOUT / GOL
After a few lines of algebra : GCIRC  -VOUT / VSRC = R2 / [ R1 + (R1 + R2) / GOL ]
eqn. 1
For GOL very large, (R1 + R2) / GOL is very small compared to R1, so GCIRC  R2 / R1
As GOL becomes smaller, the full formula must be used; the denominator increases so |G CIRC| becomes smaller.
If we define the ideal gain of the amplifier to be GIDEAL = R2 / R1 and substitute this into eqn. 1, then
GCIRC = GIDEAL x GOL / ( GOL + GIDEAL + 1)
For high GOL, the correction factor relating the actual and ideal circuit gains is nearly one. As GOL gets lower, approaching
GIDEAL, the correction factor starts falling significantly below 1, so the real circuit gain becomes less than the feedback-defined
ideal gain.
5
Minimum Circuit for Sine and Triangle Waves -- EXAR XR-2206 Waveform Generator
+15 V
Smooth internal bias voltage
1uF
Smooth Vcc 1uF
4
10
+15 V
Sine wave is centered at about
this voltage, here ~7.5 volts
5.1K
Determines amplitude of
sine wave, here ~1.6 volts
peak-to-peak
0 to 50K
Vcc
1
3
10K
1.0uF
BIAS
AMSI
MO
Frequency determined by RT and CT
Offset and amplitude determined by pin-3 circuitry
5.1K
0.1uF
CT
6
Timing capacitor CT
0.001 uF to 100 uF
Frequency 1 / RTCT
Here F = 1 / (104  10-7) = 1KHz
10K
7
RT
x
Timing resistor RT
1K to 2M
8
STO
TC1
9
13
200
14
x
15
x
16
SINE or TRIANGLE WAVE OUT
2
TC2
+15 V
Pullup resistor for open
collector square-wave output
TR1
TR2
10K
SYNCO
x
Remove resistor for
triangle wave output
5
FSKI
11
SQUARE WAVE OUT
Frequency determined by RT and CT
Varies between ~ground and ~pullup voltage
WAVEA1
WAVEA2
SYMA1
SYMA2
GND
12
6
Embellished Circuit for Sine and Triangle Waves -- EXAR XR-2206 Waveform Generator
+15 V
Smooth internal bias voltage
1uF
Smooth Vcc 1uF
4
+15 V
Vcc
Make this a 0-50K variable
resistor for amplitude control
Provide some adjustment for the
5.1K
sine wave's offset voltage.
Remember that moving this
1K
away from the midpoint voltage
(7.5 volts) reduces the maximum
sine wave amplitude.
1.0uF
5.1K
1
3
50K
CT
5
6
Switch in various capacitors
between 0.001 uF to 100 uF
Frequency 1 / RTCT
Make RT continuously
variable between 1K and
2M. You must not let
RT fall below 1K ! !
7
1K
2M
Sine waveform adjustment.
Open switch for triangle waves.
RT
x
8
BIAS
AMSI
MO
Frequency determined by RT and CT
Offset and amplitude determined by pin-3 circuitry
STO
TC1
x
500
9
13
25K
15
16
SINE or TRIANGLE WAVE OUT
2
TC2
+15 V
Pullup resistor for open
collector square-wave output
TR1
TR2
10K
SYNCO
14
Waveform symmetry adjustment.
10
FSKI
11
SQUARE WAVE OUT
Frequency determined by RT and CT
Varies between ~ground and ~pullup voltage
WAVEA1
WAVEA2
SYMA1
SYMA2
GND
12
7