Op-amp-gain error analysis
By Ron Mancini -- EDN, December 7, 2000
One of my previous columns explains a method for calculating decreasing open-loop-gain-induced errors (Reference 1). Several readers requested a simpler error-function explanation, so this one uses op-amp equations to illustrate the effect of reduced gain on accuracy.
The gain of a typical voltage-feedback op amp starts falling off at very low frequencies. Op amps have an approximate open-loop gain of 100 dB at a frequency of 10 Hz, and the op-amp gain rolls off at a rate of –20 dB/decade. The closed-loop-gain equation for a noninverting op amp is:
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where a is the op-amp gain, RF is the feedback resistor, and RG is the gain-setting resistor (Reference 2).
Let the ideal closed-loop gain, VOUT/VIN=(1+RF/RG)=2, so RF=RG. Table 1 tabulates the actual gain for each decade increase in frequency. A 2% error exists at f=10 kHz, and the circuit is usable in most applications. However, a higher bandwidth op amp reduces the error in applications with input frequencies greater than 10 kHz. The incoming signal is normally a complex waveform involving many frequencies, so it is apparent that this op amp degrades the high-frequency content of the input waveform. You don't know whether the op amp is usable until you know what portion of the input signal is degraded. As Reference 1 suggests, prudent designers must carefully analyze the input signal to get the best bang for their buck; if 0.1% of the input signal is 10 kHz or higher, then 2% of the overall degradation shouldn't hurt you at all.
The closed-loop gain for an inverting op amp is:
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The inverting-op-amp circuit complicates the situation because the RF and RG modify the op-amp gain in the numerator. Let the ideal closed-loop gain, VOUT/VIN=(–RF/RG)=–2, so RF=2RG. Table 2 tabulates the actual gain for each decade increase in frequency.
Now for the surprise: The noninverting and inverting circuits with identical ideal closed-loop gains have different error functions. The inverting circuit error is higher for equivalent ideal closed-loop gains. This situation is always the case, but at higher ideal closed-loop gains, the errors begin to merge.
The differential amplifier uses both op-amp inputs. A voltage divider (R1 and R2) and an inverting circuit precede the differential amplifier's noninverting circuit. The amplifier's gain equation is:
When R2
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RF and R1
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RG, the inverting and noninverting errors are different, and that situation can lead to unexpected distortion because the error terms are different. But, when R2=RF and R1=RG, the equation reduces to:
and the error terms are identical.
Amplifier gain falls as frequency increases, and switching to a current-feedback amplifier can minimize this physical characteristic of voltage-feedback amplifiers. The switch is not always possible because current-feedback amplifiers have lower precision. The choice usually boils down to using a higher bandwidth voltage-feedback amplifier, accepting the error, or using frequency peaking to extend the bandwidth of the circuit. Frequency peaking is better left for a future column.
Author info
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REFERENCE
1.Mancini, Ron, "Op-amp bandwidth and accuracy," EDN, Feb 17, 2000, pg 28.
2. "Stability Analysis of Voltage-Feedback Op Amps," Texas Instruments, SLOA020, July 1999.
