Op Amp Distortion

previous Total Output Noise Calculations
Dynamic range of an op amp may be defined in several ways. The most common ways are to specify harmonic distortion, total harmonic distortion (THD), or total harmonic distortion plus noise (THD + N).
Other specifications related specifically to communications systems such as intermodulation distortion (IMD), intercept points (IP), spurious free dynamic range (SFDR), multitone power ratio (MTPR) and others are covered thoroughly in Chapter 6, Section 6-4. In this section, only harmonic distortion, THD, and THD + N will be covered.
The distortion components which makes up total harmonic distortion is usually calculated by taking the root sum of the squares of the first five or six harmonics of the fundamental. In many practical situations, however, there is negligible error if only the second and third harmonics are included. The definition of THD and THD + N is shown in Figure 1-79 below.
Definitions of THD and THD + N
Figure 1-79: Definitions of THD and THD + N
It is important to note that the THD measurement does not include noise terms, while THD + N does. The noise in the THD + N measurement must be integrated over the measurement bandwidth. In audio applications, the bandwidth is normally chosen to be around 100kHz. In narrow-band applications, the level of the noise may be reduced by filtering.
On the other hand, harmonics and intermodulation products which fall within the measurement bandwidth cannot be filtered, and therefore may limit the system dynamic range.
Common-Mode Rejection Ratio (CMRR), Power Supply Rejection Ratio (PSRR)
If a signal is applied equally to both inputs of an op amp, so that the differential input voltage is unaffected, the output should not be affected. In practice, changes in common-mode voltage will produce changes in output. The op amp common-mode rejection ratio (CMRR) is the ratio of the common-mode gain to differential-mode gain. For example, if a differential input change of Y volts produces a change of 1V at the output, and a common-mode change of X volts produces a similar change of 1V, then the CMRR is X/Y. When the common-mode rejection ratio is expressed in dB, it is generally referred to as common-mode rejection (CMR). Typical LF CMR values are between 70 and 120dB, but at higher frequencies, CMR deteriorates. Many op amp data sheets show a plot of CMR versus frequency, as shown in Figure 1-80 for an OP177 op amp.
OP177 common-mode rejection (CMR)
Figure 1-80: OP177 common-mode rejection (CMR)
CMRR produces a corresponding output offset voltage error in op amps configured in the non-inverting mode as shown in Figure 1-81 below.
Calculating offset error due to common-mode rejection ratio (CMRR)
Figure 1-81: Calculating offset error due to common-mode rejection ratio (CMRR)
Note inverting mode operating op amps will have negligible CMRR error, as both inputs are held at a ground (or virtual ground), i.e., there is no CM dynamic voltage.
Common-mode rejection ratio can be measured in several ways. The method shown in Figure 1-82 below uses four precision resistors to configure the op amp as a differential amplifier, a signal is applied to both inputs, and the change in output is measured— an amplifier with infinite CMRR would have no change in output. The disadvantage inherent in this circuit is that the ratio match of the resistors is as important as the CMRR of the op amp. A mismatch of 0.1% between resistor pairs will result in a CMR of only 66dB— no matter how good the op amp! Since most op amps have a LF CMR of between 80 and 120dB, it is clear that this circuit is only marginally useful for measuring CMRR (although it does an excellent job in measuring the matching of the resistors!).
Simple common-mode rejection ratio (CMRR) test circuit
Figure 1-82: Simple common-mode rejection ratio (CMRR) test circuit
The slightly more complex circuit shown in Figure 1-83 below measures CMRR without requiring accurately matched resistors. In this circuit, the common-mode voltage is changed by switching the power supply voltages. (This is easy to implement in a test facility, and the same circuit with different supply voltage connections can be used to measure power supply rejection ratio).
CMRR test circuit does not require precision resistors
Figure 1-83: CMRR test circuit does not require precision resistors
The power supply values shown in the circuit are for a ±15V DUT op amp, with a common-mode voltage range of ±10V. Other supplies and common-mode ranges can also be accommodated by changing voltages, as appropriate. The integrating amplifier A1 should have high gain, low VOS and low IB, such as an OP97 family device.
If the supply of an op amp changes, its output should not, but it does. The specification of power supply rejection ratio or PSRR is defined similarly to the definition of CMRR. If a change of X volts in the supply produces the same output change as a differential input change of Y volts, then the PSRR on that supply is X/Y. The definition of PSRR assumes that both supplies are altered equally in opposite directions—otherwise the change will introduce a common-mode change as well as a supply change, and the analysis becomes considerably more complex. It is this effect which causes apparent differences in PSRR between the positive and negative supplies.
OP177 power supply rejection
Figure 1-84: OP177 power supply rejection
Typical PSR for the OP177 is shown in Figure 1-84 above.
The test setup used to measure CMRR may be modified to measure PSRR as shown in Figure 1-85 below.
Test setup for measuring power supply rejection ratio (PSRR)
Figure 1-85: Test setup for measuring power supply rejection ratio (PSRR)
The voltages are chosen for a symmetrical power supply change of 1V. Other values may be used where appropriate.
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