A Simple "Guide" to Measuring Operational Amplifier Parameters

The measurement process can be greatly simplified by using a servo loop to force the amplifier inputs to zero, allowing the amplifier under test to measure its own errors. Figure 1 shows a versatile circuit that uses this principle, using an auxiliary op amp as an integrator to create a stable loop with very high dc open-loop gain. Switches facilitate the various tests described below.

Figure 1. Basic op amp measurement circuit.

The circuit shown in Figure 1 minimizes most measurement errors and allows accurate measurement of a wide range of dc and a small number of ac parameters. The additional “helper” op amp does not need to have better performance than the op amp under test, but a dc open-loop gain of 106 or greater is preferred. If the offset voltage of the device under test (DUT) can exceed a few mV, the helper op amp should be powered from ±15 V supplies. (If the input offset voltage of the DUT can exceed 10 mV, the value of the 99.9 kΩ resistor R3 needs to be reduced.)

The DUT's supply voltages, +V and –V, are equal in magnitude and opposite in polarity. The total supply voltage is, of course, 2 × V. This circuit uses symmetrical supplies, even for “single-supply” op amps, because the system ground is referenced to the middle of the supplies.

The voltage at test point TP1 is 1000 times the correction voltage (equal in magnitude to the error) applied to the DUT input, which is on the order of tens of mV or more, so it can be measured fairly easily.

_{The offset voltage (V os} ) of an ideal operational amplifier is 0, that is, when the two input terminals are connected together and maintained at the mid-supply voltage, the output voltage is also at the mid-supply voltage. Real operational amplifiers have offset voltages ranging from a few microvolts to a few millivolts, so a voltage within this range must be applied to the input terminals to keep the output at the mid-potential.

Figure 2 shows the configuration for the most basic test, offset voltage measurement. When the voltage on TP1 is 1000 times the DUT offset voltage, the DUT output voltage is at ground potential.

Figure 2. Offset voltage measurement.

An ideal op amp has infinite input impedance, with no current flowing into its inputs. In reality, however, small amounts of “bias” current flow into the inverting and noninverting inputs (I _b– and I _b+ , respectively ), which can cause significant offset voltages in high-impedance circuits. Depending on the type of op amp, this bias current can range from a few fA (1 fA = 10 ^–15 A, with one electron flowing every few microseconds) to a few nanoamps; in some ultrafast op amps, it can even reach 1 - 2 μA. Figure 3 shows how to measure these currents.

Figure 3. Offset and bias current measurements.

This circuit is essentially the same as the offset voltage circuit of Figure 2, except that two series resistors, R6 and R7, are added to the DUT input. These resistors can be shorted by switches S1 and S2. When both switches are closed, the circuit is exactly the same as Figure 2. When S1 is open, the bias current at the inverting input flows into Rs, and the voltage difference is added to the offset voltage.

By measuring the voltage change at TP1 (=1000 I _b –×R _{s ), I b–} can be calculated . Similarly, when S1 is closed and S2 is open, I _{b+ can be measured. If the voltage at TP1 is first measured when both S1 and S2 are closed, and then measured again when both S1 and S2 are open, the "input offset current" I os} can be calculated from the voltage change , which is the difference between I _b+ and I _b– . The resistance values ​​of R6 and R7 depend on the current to be measured.

The open-loop dc gain of an op amp can be very high; gains of more than 10 ⁷ are not uncommon, but gains of 250,000 to 2,000,000 are more common. The dc gain is measured by switching R5 between the DUT output and a 1 V reference voltage via S6, forcing the DUT output to change by a certain amount (1 V in Figure 4, but 10 V can be specified if the device is powered from a sufficiently large supply). If R5 is at +1 V, the DUT output must go to –1 V in order for the auxiliary amplifier input to remain constant near 0.

Figure 4. DC gain measurement.

The voltage change at TP1 is attenuated 1000:1 before being input to the DUT, resulting in a 1 V change at the output, from which the gain can be easily calculated (= 1000 × 1 V/TP1).

To measure the open-loop AC gain, a small AC signal of the desired frequency is injected at the DUT input and the corresponding output signal is measured (TP2 in Figure 5). Once this is done, the auxiliary amplifier continues to keep the average DC level at the DUT output stable.

Figure 5. AC gain measurement.

In Figure 5, an ac signal is applied to the DUT input via a 10,000:1 attenuator. Such large attenuation values ​​are necessary for low-frequency measurements where the open-loop gain may be close to the dc value. (For example, at a gain of 1,000,000, a 1 V rms signal will apply 100 μV to the amplifier input, and the amplifier will saturate as it attempts to provide 100 V rms output.) Therefore, ac measurements are typically made from a few hundred Hz to the frequency where the open-loop gain drops to 1; when low-frequency gain data is needed, great care should be taken to measure with lower input amplitudes. The simple attenuator shown will only work to frequencies below 100 kHz, even if care is taken to account for stray capacitance. If higher frequencies are involved, more complex circuits will be required.

The common-mode rejection ratio (CMRR) of an op amp is the ratio of the apparent change in offset voltage due to a change in common-mode voltage to the change in applied common-mode voltage. It is typically between 80 dB and 120 dB at DC, but decreases at high frequencies.

The test circuit is well suited for measuring CMRR (Figure 6). Rather than applying a common-mode voltage to the DUT inputs, where low-level effects would corrupt the measurement, the supply voltage is varied (in the same direction relative to the inputs, i.e., the common-mode direction), while the rest of the circuit remains unchanged.

Figure 6. DC CMRR measurement.

In the circuit of Figure 6, the offset voltage is measured at TP1 with the supplies at ±V (+2.5 V and –2.5 V in this case) and both supplies shifted up by +1 V again (to +3.5 V and –1.5 V). A change in the offset voltage corresponds to a 1 V change in the common-mode voltage, so the dc CMRR is the ratio of the offset voltage to 1 V.

CMRR is a measure of the change in offset voltage relative to the change in common-mode voltage, with the total supply voltage held constant. The power supply rejection ratio (PSRR) is the opposite and is the ratio of the change in offset voltage to the change in total supply voltage, with the common-mode voltage held constant at midsupply (Figure 7).

Figure 7. DC PSRR measurement.

The circuit used is exactly the same, except that the total supply voltage is changed while the common-mode level remains the same. In this case, the supply voltages are switched from +2.5 V and –2.5 V to +3 V and –3 V, and the total supply voltage is changed from 5 V to 6 V. The common-mode voltage remains midsupply. The calculation is also the same (1000 × TP1/1 V).

To measure the ac CMRR and PSRR, the supply voltage is modulated with a voltage, as shown in Figures 8 and 9. The DUT continues to operate in a dc open loop, but the exact gain is determined by the ac negative feedback (100 times in the figure).

Figure 8. AC CMRR measurement.

Figure 9. AC PSRR measurement

To measure the ac CMRR, the positive and negative supplies to the DUT are modulated with an ac voltage of 1 V peak amplitude. The two supplies are modulated in phase, so the actual supply voltages are stable dc voltages, but the common-mode voltage is a 2 V peak-to-peak sine wave, causing the DUT output to include an ac voltage measured at TP2.

If the ac voltage at TP2 has an amplitude of x V peak (2x V peak-to-peak), then the CMRR referred to the DUT input (that is, before the 100x ac gain) is x/100 V, and the CMRR is the ratio of this value to 1 V peak.

AC PSRR is measured by applying an AC voltage to the positive and negative supplies 180° out of phase, thereby modulating the amplitude of the supply voltage (again, 1 V peak, 2 V peak-to-peak in this case), while the common-mode voltage remains a steady DC voltage. The calculation is very similar to the previous parameter.