Real World Op-Amp Behavior Vs. Ideal Models

Real-World Op-Amp Limitations

Input Offset Voltage

The input offset voltage is the differential voltage that must be applied between the input terminals of the operational amplifier to make the output voltage equal to zero. In an ideal op-amp, this offset voltage is zero. However, real-world op-amps exhibit a small but nonzero input offset voltage typically in the range of a few millivolts. Possible causes include transistor mismatches, leakage currents, temperature gradients, and noise. The input offset voltage introduces a small output error voltage even when the input differential voltage is zero. Compensating techniques include nulling circuits, chopper stabilization, and auto-zeroing.

Input Bias Current

The input bias current is the average of the currents entering the two input terminals of the op-amp. The ideal op-amp draws no input current, but real-world op-amps have a small bias current flowing into the inputs, typically ranging from femtoamps to picoamps. This current flowing through any resistance at the inputs creates an unwanted input voltage that can lead to output errors. Compensation methods include using FET input op-amps with lower input currents or adding bias current cancellation resistors.

Input Impedance

An ideal operational amplifier has infinite input impedance, meaning it appears as an open circuit to any external circuitry connected to the input terminals. However, practical op-amps have a high but finite input impedance, typically between 1 and 10 megaohms. This can attenuate high-impedances sources at the input and reduce noise performance. Careful buffering of the input sources can minimize the loading effects from finite input impedance.

Common-Mode Rejection Ratio (CMRR)

The CMRR indicates an op-amp’s ability to reject common-mode signals – signals that appear simultaneously and in-phase on both input terminals. An ideal op-amp would have infinite CMRR. However, real op-amps have CMRR limitations caused by resistor mismatches, transistor imbalances, and power supply noise coupling. Typical CMRR values range from 70-120 dB. Poor CMRR can allow more common-mode noise into the amplification circuit. Improving CMRR requires careful IC design, layout, and power supply decoupling.

Output Resistance

While an ideal op-amp has zero output impedance, practical op-amps have a finite, low-value output resistance, usually less than 500 ohms. This resistance appears in series with the load impedance, forming an undesired voltage divider that attenuates the load voltage. Low output resistance op-amps, buffer stages, or negative feedback can minimize loading effects on the output.

Output Current Limitations

Real-world operational amplifiers can only source and sink a limited output current, ranging from milliamps to hundreds of milliamps based on the device specs. Exceeding these limits causes clipping or saturation of the output voltage. Sizing the op-amp to handle the required load currents prevents distortion. Parallel transistor stages or buffer amplifiers can provide additional output current drive.

Frequency Response

While an ideal op-amp has an infinite bandwidth, practical devices have frequency limitations. At higher frequencies, the open-loop gain starts rolling off at -20 dB/decade due to internal capacitances. Moreover, the GBW product (gain-bandwidth product) imposes a tradeoff between voltage gain and frequency response. Careful pole-zero placement via negative feedback networks allows extending the usable frequency range.

Settling Time

The settling time specifies how long it takes for the op-amp output to settle to within a certain error band of its final value after an input change. Real op-amps may have substantial settling times, ranging from nanoseconds to microseconds based on amplifier topology, creating delays in reaching a final, accurate output value. Design techniques like pole splitting can minimize settling time for improved dynamic response.

Example Circuits and Calculations

Inverting Amplifier with Non-Ideal Input Impedance

An inverting amplifier using negative feedback sets the closed-loop gain to Rf/Ri, assuming ideal op-amps. However, practical op-amps have non-zero and finite input impedance. This additional impedance appears in series with Ri, modifying the overall input impedance and actual gain. Detailed calculations show that the overall gain becomes Rf/(Ri + Zin) where Zin is the input impedance. If Zin is 1 MΩ and Ri is 10 kΩ, the added impedance modifies the expected gain of -10 into an actual gain of -9.9. Careful buffering of the input can render Zin negligible.

Difference Amplifier with Imperfect CMRR

A difference amplifier amplifies the voltage difference between two input signals while rejecting any signals common to both inputs. This relies on the CMRR property of operational amplifiers. However, as analyzed above, real op-amps have finite CMRR limitations around 70-120 dB. For a CMRR of 100 dB, a common-mode input signal couples 0.001% or 1/100,000 into the output – substantial for small differential input signals. Improving CMRR requires noise reduction on power supplies along with precision resistor matching and transistor layout schemes.

Non-Inverting Amplifier with Limited Bandwidth

The non-inverting op-amp configuration applies feedback in parallel with the input source resistance unlike the inverting case. This avoids input loading effects from finite input impedance. However, practical op-amps have bandwidth limitations based on internal compensation capacitance and the GBW tradeoff between gain and frequency response. Detailed analysis of a non-inverting circuit with typical GBW values demonstrates that the high closed-loop gain diminishes unity-gain bandwidth substantially. Additional external compensation networks added to the feedback path can restore overall frequency response.

Compensating for Non-Ideal Op-Amp Behavior

Using Negative Feedback

Negative feedback is the most powerful, flexible technique for compensating non-ideal op-amp characteristics. Input impedance, output impedance, common-mode signals, and frequency effects can all be minimized using appropriate feedback resistor networks. Negative feedback lowers overall gain proportional to the amount of feedback but dramatically improves linearity, dynamic response, and robustness to parameter variations.

Selecting Appropriate Op-Amps

Choosing the right operational amplifier optimized for parameters critical to the application – input bias current, power bandwidth, output resistance, etc. – can minimize the impact of non-ideal behavior overall. Precision op-amps offer premium performance specifications albeit at increased cost. Evaluating design tradeoffs allows picking the least expensive op-amp to meet requirements.

Adding Supporting Circuitry

Supporting active and passive components can overcome op-amp limitations in specialized applications. Input buffer stages isolate bias currents; output transistor followers boost load drive capability. Emitter followers using transistors also provide low-impedance outputs. Precision metal-film resistors and potentiometers trim out input offset voltages. Overall, external circuitry can bolster weak op-amp performance areas.

Simulation for Verification

Modern analog circuit simulators allow inputting real-world op-amp parameters to predict non-ideal circuit behavior during the design phase itself. Performing Monte Carlo statistical analysis shows the impact of component variability also. This prevents costly redesign cycles later and ensures robust operation despite inevitable op-amp imperfections. Worst-case modelling guarantees specifications compliance over all operating conditions.