Non-ideal op-amps
0. Introduction
In our analysis of circuits based on the operational amplifier, we made a
number of important assumptions:
a. The input currents are zero.
b. The gain of the op-amp is infinite for all frequencies.
c. There are no input offset voltages, i.e., in a properly working circuit V+ V- = 0.
d. The op-amp output impedance is zero, and the output voltage can change
at any rate, e.g., in response to a steep step of an input voltage dVout/dt
→ ∞.
e. There is no noise.
Although modern op-amps approximate some of these ideal properties quite
well, a single device usually does not satisfy them all simultaneously. For
example, an op-amp may be quite fast, but have a significant offset voltage,
or, a device may have extremely low voltage noise, but large input currents.
The following exercises are intended to give you some intuition for certain
types of non-ideal behavior, as well as for what can be achieved with
generally available op-amps.
1. Input offset voltage and noise
Assemble a non-inverting amplifier with a gain of 1000, Fig. 1, and ground the
non-inverting input. The amplifier now amplifies its own noise, Vnoise, and input
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Non-ideal op-amps
offset voltage, Vo. Measure Vo using your DMM, and with the help of an
oscilloscope, estimate Vnoise. Do this for three different op-amps, the
LM741, OP27 and LT1792. Note not only the difference in magnitude of the
noise but also its spectral characteristics.
Figure 1. Offset and noise
2. Input currents
To measure the input current you can connect a resistor, Rin, between the
non-inverting input and ground. The current into the input causes a voltage
drop across Rin, which is amplified in the same way as Vo. The input current,
Ibias is given by Ibias = ∆Vout/(1000×Rin), where ∆Vout is the difference in the
output voltage with Rin shorted or not shorted. Op-amps with FET inputs
have an Ibias that is so small that this method becomes less practical.
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Non-ideal op-amps
Instead of measuring the voltage drop across a resistor, one can monitor the
change in voltage across a capacitor as it is charged by the bias current. In
this case Ibias = C×(∆Vout/1000)/∆t, with ∆Vout the change in the output
voltage over the measuring time ∆t.
Determine the input bias currents for the LM741, OP27 and LT1792.
Figure 2a. Determining the bias current for the LM741 and OP27
Figure 2b. Determining the bias current for the LT1792
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Non-ideal op-amps
3. Gain-bandwidth product
A convenient number to characterize an op-amp is its gain-bandwidth
product. It tells you directly which bandwidth can be realized for which
closed loop gain. To look at this, determine the small signal frequency
response for non-inverting amplifiers with gains of 10, 100 and 1000, based
on the OP27. What do you obtain for the gain-bandwidth product?
4. Transient response and slew rate
The transient response, i.e., the response to a step or pulse, of an amplifier
is determined by the frequency response of the op-amp, as well as that of
the feedback loop. With amplifiers configured for a high closed loop gain,
one will primarily see the effect of the limited over all bandwidth. The
response to a step will have an exponential shape with a rise time τ = 1/2πfc
(fc is the 3dB bandwidth). With low gain amplifiers the details of the
feedback circuit become important, as well as the behavior of the op-amp at
high frequency. Stray capacitance can cause phase shifts that make the
circuit unstable.
First, construct an amplifier with a gain of +2 (Fig 3). Apply a square wave,
100 kHz, 100 mV signal to the input and compare input and output signals.
Do this for the LM741 and the LT1792. The oscillations observed with the
LT1792 can be eliminated with a small capacitor parallel to the feedback
resistor
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Non-ideal op-amps
Figure 3.
A circuit to determine the transient response
Secondly, increase the gain of the amplifier to 10, and again compare the
behavior of the circuit with an LM741 and an LT1792. It should be clear that
while the LT1792 can follow the input signal with ease, the LM741 is now too
slow. Finally, still with an amplifier gain of ten, look at what happens when
the signal amplitude is increased. For small amplitude, you should observe a
well defined, amplitude independent, rise time for the LM741. When the
input voltage exceeds 200 mV the character of the output voltage starts to
change. It now appears that the voltage can only change at a fixed rate,
independent of the amplitude at the input. This rate is called the slew rate.
Try to repeat this with the LT1792. Only very close to the point where the
output gets completely saturated will you see deviation from “ideal”
behavior.
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Non-ideal op-amps