*Op Amp Integrator*
CIRCUIT
OPINT.CIR
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SPICE file
The integrator basically works like this: whatever
current I you get flowing in R1, gets integrated across capacitor C1. The
output voltage Vo is simply the voltage across C1. One great application of
the integrator is generating a ramp voltage. You can do this by placing a
fixed voltage at VS that forces a constant current through R1. The capacitor
then integrates this current creating a ramping voltage. The action is just
like a garden hose running water at a constant rate causing the level in a
bucket to rise steadily. The smaller the diameter bucket (smaller
capacitor), the faster the increase in water level (greater voltage). The
switch is needed to discharge the capacitor (empty the bucket) at the end of
a ramping cycle.
RAMP GENERATOR
The circuit essentially integrates the input current Is
= VS / R1 across capacitor C1. After a time interval T, the output is the
capacitor voltage
described by
If you apply a constant voltage at VS, the output
voltage increases steadily (ramp). You can predict the ramp's voltage at any
time T by the simplified equation
CIRCUIT ANALYSIS
Try the circuit. What is the output voltage V(3) after 100us? With
VS= -1, R1=10k and C1 = 1nF, the output should be Vo = -1/1nF x
(-1/ 10k) x 100us = 1V.
Look at the switch control voltage VRESET at V(4). VRESET turns
the switch OFF (VRESET=0V) and ON (VRESET=5V). Switch S1 is initially OFF.
After 100us, S1 turns ON discharging the capacitor for 10us. Then, the
ramping cycle begins again.
HANDS-ON DESIGN
Design a circuit that ramps faster or slower than the original
circuit. The equation above tells you that you can change VS, R1 or C1 to
achieve your goal. (Example: For a slower ramp that reaches only 5V in 100us, make
R1 equal to 2x its initial value. This cuts the current through R1 by ½
decreasing the ramp rate by ½. ) You may have noticed that this is an
inverting circuit; a negative VS creates a positive output. Need to create
a create a negative ramp? Apply a positive VS.
SWITCH RESISTANCE
How important are the ON and OFF resistances of the
switch in this application? Return the circuit to its original values
(R1=10k, C1=1000pF, and VS=-1).
CIRCUIT INSIGHT
Suppose you had
a switch with an OFF resistance that‘s too small. What would happen to ramp
voltage? Reduce the OFF resistance from 10MEG to a smaller value like 1MEG
by modifying the switch model statement
.MODEL SRES VSWITCH(VON=0 VOFF=5 RON=100
ROFF=1MEG)
Try the circuit and plot the output V(3). Did the
output reach your expected value? A smaller ROFF may discharge C1
significantly during the ramping interval.
What about an ON resistance that’s too large during the
reset interval? Return ROFF to its initial value and increase RON from 100
to 1000.
.MODEL SRES VSWITCH(VON=0 VOFF=5
RON=1000 ROFF=10MEG)
Run the circuit. Did capacitor C1 discharge fully in
the reset interval? What happens if RON is even larger like 10000?
SIMULATION NOTE
SPICE’s source statement named PULSE is a convenient
way to generate a repeating pulsed waveform according to syntax
PULSE( {v1} {v2} {tdelay} {trise} {tfall} {width} {period} ).
So the statement
VRESET 4 0 PULSE(0V 5V 0 0.1US 0.1US
100US 110US)
creates a repeating pulse from VRESET
that’s defined by 0V for 100us and 5V for 10us for a total period of 110us.
The rise and fall times are 0.1 us.
SPICE FILE
Download the file
or copy this netlist into a text file with the *.cir
extention.
OPINT.CIR - OPAMP INTEGRATOR
*
* CONTROL VOLTAGE FOR S1
VRESET 4 0 PULSE(0V 5V 0 0.1US 0.1US 100US 110US)
R4 4 0 1MEG
*
* INPUT VOLTAGE
VS 1 0 DC -1
*
R1 1 2 10K
C1 2 3 1000PF
S1 2 3 4 0 SRES
XOP 0 2 3 OPAMP1
*
.MODEL SRES VSWITCH(VON=0 VOFF=5 RON=100 ROFF=10MEG)
*
* OPAMP MACRO MODEL, SINGLE-POLE
* connections: non-inverting input
* | inverting input
* | | output
* | | |
.SUBCKT OPAMP1 1 2 6
* INPUT IMPEDANCE
RIN 1 2 10MEG
* GAIN BW PRODUCT = 10MHZ = DCGAIN x POLE1
* DC GAIN (100K) AND POLE 1 (100HZ)
EGAIN 3 0 1 2 100K
RP1 3 4 1K
CP1 4 0 1.5915UF
* OUTPUT BUFFER AND RESISTANCE
EBUF 5 0 4 0 1
ROUT 5 6 10
.ENDS
*
* ANALYSIS
.TRAN 1US 220US
* VIEW RESULTS
.PLOT TRAN V(1) V(3)
.PRINT TRAN V(1) V(3)
.PROBE
.END
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