Electronics Guide

Circuit Operation

In the inverting configuration, the op-amp maintains its inverting input at virtual ground potential. Because the non-inverting input connects to actual ground and the op-amp has extremely high gain, the voltage difference between the two inputs approaches zero. Current flowing through the input resistor must equal the current through the feedback resistor (the high input impedance of the op-amp prevents any significant current from entering its inputs), creating a precise relationship between input and output voltages.

The voltage gain of an inverting amplifier is:

Av = -Rf / Rin

where Rf is the feedback resistor and Rin is the input resistor. The negative sign indicates the phase inversion inherent to this configuration.

Design Considerations

The input impedance of an inverting amplifier equals the input resistor value, which may be insufficient for high-impedance sources. Selecting larger resistor values increases input impedance but also increases thermal noise and may introduce errors due to input bias currents.

For gains less than unity, the inverting configuration excels because it can easily achieve attenuation while maintaining a defined input impedance. Unity gain occurs when Rf equals Rin, while gains less than one require Rf smaller than Rin.

The virtual ground at the inverting input makes this configuration ideal for summing multiple signals, as each input sees only its own input resistor rather than interacting with other input sources.

Common Applications

• Signal amplification with controlled gain
• Signal attenuation and scaling
• Phase inversion in audio and signal processing
• Building block for summing amplifiers
• Active filter implementations

Circuit Operation

With the input applied to the non-inverting terminal, the op-amp adjusts its output to maintain virtually zero voltage difference between its inputs. This forces the voltage at the inverting input to equal the input signal voltage, and the resistive divider between output and ground must produce this voltage at its midpoint.

The voltage gain of a non-inverting amplifier is:

Av = 1 + (Rf / R1)

where Rf is the feedback resistor and R1 is the resistor from the inverting input to ground. This formula shows that the minimum gain is unity (when Rf equals zero), making the non-inverting configuration unsuitable for attenuation.

Design Considerations

The input impedance of a non-inverting amplifier is extremely high, approaching the op-amp's own input impedance multiplied by the loop gain. This makes the configuration ideal for buffering high-impedance sources without loading them.

Input bias current flows through the source impedance, potentially creating offset errors. To minimize this effect, some designs add a resistor between the non-inverting input and ground equal to the parallel combination of Rf and R1, balancing the bias current effects at both inputs.

Common-mode voltage handling becomes a consideration because the entire input signal appears at the op-amp's inputs. The selected op-amp must have adequate common-mode input range for the expected signal levels.

Common Applications

• High-impedance buffer amplification
• Sensor signal conditioning
• Voltage scaling without inversion
• Input stages for precision instruments
• Audio preamplifiers

Circuit Characteristics

With 100% negative feedback, the voltage follower exhibits unity gain (Av = 1) with extremely high input impedance and low output impedance. The output precisely follows the input voltage, limited only by the op-amp's ability to drive the load and its finite bandwidth and slew rate.

The voltage follower isolates the source from the load, preventing loading effects that would otherwise reduce signal amplitude. A high-impedance sensor can drive the follower's input while the op-amp's output stage drives low-impedance loads without affecting the sensor.

Performance Limitations

While conceptually simple, voltage followers present stability challenges in certain situations. The direct feedback connection provides no frequency-dependent roll-off, potentially causing oscillation with capacitive loads or long cable runs. Many op-amps require compensation or isolation resistors when driving significant capacitive loads.

Input offset voltage and input bias current directly affect output accuracy since there are no resistors to introduce additional errors but also no gain to amplify them. For precision applications, selecting op-amps with low offset and bias specifications proves essential.

Buffer Variations

Several variations on the basic voltage follower address specific application requirements:

• AC-coupled follower: Capacitor in series with the input blocks DC while passing AC signals
• Bootstrapped buffer: Increased input impedance through positive feedback to the power supply decoupling
• Composite buffer: Output transistor stage adds current drive capability
• Differential buffer: Converts differential signals to single-ended output

Operating Principles

Because the inverting input maintains virtual ground potential, each input resistor operates independently: the current from each source depends only on its voltage and resistor value, unaffected by other inputs. All input currents combine at the summing junction and flow through the feedback resistor, producing an output voltage proportional to their sum.

For a summing amplifier with n inputs:

Vout = -Rf (V1/R1 + V2/R2 + V3/R3 + ... + Vn/Rn)

Equal input resistors produce a simple sum (or average, if scaled appropriately), while different resistor values weight the inputs differently.

Design Considerations

The summing amplifier's virtual ground isolates inputs from each other, preventing interaction between sources. This makes it ideal for audio mixing applications where multiple signals must combine without crosstalk.

Each input sees only its own input resistor as impedance, regardless of other inputs or their impedances. This predictable loading simplifies interface design between multiple signal sources.

The total input current capability limits the number of inputs and their gains. Too many inputs with low resistor values may exceed the output current capability of the feedback network or cause excessive noise.

Weighted Summation

Varying the input resistor values creates weighted sums useful for scaling signals before combining. For example, in an audio mixer, different channels may require different gain factors to balance levels from various sources like microphones, instruments, and playback devices.

Digital-to-analog converters often use summing amplifier principles with binary-weighted resistors, where each input resistor doubles in value for each bit position. This converts a digital binary code into a proportional analog voltage.

Basic Configuration

The single-op-amp difference amplifier uses four resistors: two form an inverting amplifier from one input, while two form a voltage divider that sets the reference voltage at the non-inverting input from the other signal. When all four resistors are equal, the circuit produces the simple difference of the two inputs:

Vout = (V2 - V1) when R1 = R2 = R3 = R4

For differential gain, the resistor ratios determine the amplification factor while maintaining balanced response to common-mode signals.

Common-Mode Rejection

The difference amplifier's ability to reject common-mode signals depends critically on resistor matching. Any mismatch causes the common-mode voltage to appear partially in the output, reducing the common-mode rejection ratio (CMRR).

With standard 1% resistors, achievable CMRR typically ranges from 40 to 60 dB. Higher CMRR requires precision resistors with 0.1% or better matching, or integrated difference amplifiers with laser-trimmed resistors achieving 80 dB or more.

Input Impedance Considerations

Unlike the instrumentation amplifier, the simple difference amplifier presents different impedances to its two inputs, and these impedances vary with the common-mode voltage. The inverting input sees the input resistor impedance, while the non-inverting input sees the divider resistance.

This impedance imbalance can cause errors when source impedances are significant or unequal. Buffering both inputs with voltage followers before the difference amplifier addresses this limitation while maintaining the basic topology's simplicity.

Three-Op-Amp Topology

The classic instrumentation amplifier uses two input buffer stages followed by a difference amplifier. The input op-amps connect in a unique configuration that provides gain while maintaining high input impedance: a single resistor bridges their inverting inputs, with feedback resistors connecting each op-amp's output back to its inverting input.

This arrangement amplifies differential signals while passing common-mode signals through unchanged (at unity gain). The output difference amplifier then removes the common-mode component while providing additional gain or simply unity-gain subtraction.

Total Gain = (1 + 2R/Rg) for the input stage, multiplied by the difference amplifier gain

Advantages Over Simple Difference Amplifiers

• High input impedance: Both inputs see the input impedance of their respective buffer op-amps
• Balanced inputs: Both input paths are symmetric, improving CMRR
• Single-resistor gain control: Adjusting Rg changes gain without affecting CMRR
• Excellent CMRR: Proper design achieves 100 dB or higher CMRR
• Low drift: Matched input stages minimize offset voltage temperature drift

Integrated Instrumentation Amplifiers

Modern integrated instrumentation amplifiers contain all three op-amps plus precisely matched internal resistors on a single chip. These devices offer superior performance compared to discrete implementations due to tight resistor matching and thermal tracking.

Features often include programmable gain through external resistor or pin-strapping, reference voltage inputs for level shifting, and specifications optimized for specific applications like medical instrumentation, strain gauge interfaces, or thermocouple amplifiers.

Basic Transimpedance Amplifier

The simplest current-to-voltage converter connects the current source to the inverting input with only a feedback resistor to the output. The non-inverting input connects to ground (or a reference voltage). The op-amp maintains virtual ground at its inverting input, so the input current flows entirely through the feedback resistor.

Vout = -Iin x Rf

The transimpedance (transfer impedance) equals the feedback resistor value, expressed in volts per ampere (or ohms).

Photodiode Amplifiers

Photodiode current-to-voltage conversion presents unique challenges due to the photodiode's junction capacitance and the high gains typically required. The feedback resistor and photodiode capacitance form a pole in the feedback network that can cause instability.

Compensation typically involves adding a small capacitor in parallel with the feedback resistor. This capacitor value must be carefully chosen to maintain stability while preserving adequate bandwidth for the application. The optimal value depends on the feedback resistor, photodiode capacitance, and op-amp gain-bandwidth product.

Design Trade-offs

Higher feedback resistance increases sensitivity but also increases noise and reduces bandwidth. The Johnson noise of the feedback resistor often dominates in high-gain configurations, requiring careful optimization between sensitivity and noise performance.

For very low current levels (picoampere range), junction FET-input or CMOS op-amps with femtoampere-level input bias currents become necessary to prevent the op-amp's bias current from overwhelming the signal current.

Grounded-Load Converter

When the load connects to ground, a simple inverting amplifier configuration with the load in the feedback path creates a voltage-controlled current source. The op-amp maintains the current through a sensing resistor equal to the input voltage divided by the sensing resistance:

Iload = Vin / Rsense

This topology works well when one terminal of the load can connect to ground, but fails for floating loads.

Floating-Load Converter

For loads that cannot connect to ground, the Howland current pump uses two op-amps or a single op-amp with careful resistor matching. One configuration places the load between two op-amp outputs, with each op-amp controlling one end of the current path.

An alternative uses a single op-amp with both positive and negative feedback paths. The negative feedback establishes the current while positive feedback compensates for load voltage variations. Proper resistor matching is critical for accuracy and stability.

Current Loop Applications

Industrial 4-20 mA current loop transmitters commonly use voltage-to-current converters. The input voltage from a sensor signal chain converts to a current that transmits over long cable runs immune to voltage drops and noise pickup. The current range (4 mA to 20 mA) ensures a live zero allowing detection of broken wiring.

Logarithmic Amplifier Principles

The logarithmic relationship between current and voltage in a forward-biased diode or transistor junction provides the basis for log amplifiers. Placing a transistor in the feedback path of an inverting amplifier creates an output proportional to the logarithm of the input current:

Vout = -kT/q x ln(Iin/Is)

where kT/q is the thermal voltage (approximately 26 mV at room temperature) and Is is the transistor saturation current.

Because the logarithm of voltage requires first converting voltage to current (through an input resistor), the complete log amplifier equation becomes:

Vout = -kT/q x ln(Vin/(Is x Rin))

Temperature Compensation

The thermal voltage kT/q varies directly with absolute temperature, causing the log amplifier gain to change by approximately 0.3% per degree Celsius. Additionally, the saturation current Is varies exponentially with temperature.

Practical log amplifiers use matched transistor pairs and temperature compensation networks to stabilize performance. Some designs use a second transistor in a feedback loop that tracks temperature variations, while others employ temperature-dependent gain elements to compensate the thermal voltage variation.

Antilog Amplifiers

The antilogarithmic amplifier places the diode or transistor junction at the input rather than in the feedback path. The exponential relationship between voltage and current in the junction produces an output current (and through a resistor, an output voltage) that is the exponential (antilog) of the input voltage.

Combined with log amplifiers, antilog circuits enable analog computation of multiplication, division, powers, and roots. Two input voltages converted to logarithms can be added (for multiplication) or subtracted (for division), then converted back through an antilog stage.

Applications

• Dynamic range compression: Compressing signals spanning many decades into a manageable voltage range
• Analog computation: Multiplication, division, and power functions
• Signal level measurement: dB-scaled outputs for audio and RF applications
• Linearization: Compensating for exponential sensor characteristics
• True RMS conversion: As part of implicit RMS computation circuits

Half-Wave Precision Rectifier

The simplest precision rectifier uses one op-amp and one or two diodes in the feedback path. During positive input half-cycles, the diode conducts, and the circuit operates as a unity-gain (or amplifying) follower. During negative half-cycles, the feedback loop opens, and the output remains at zero (or the reverse diode clamps it).

The op-amp compensates for the diode's forward voltage by adjusting its output to whatever level necessary to make the voltage across the load follow the input. Only microvolts of input can produce accurate rectification.

Full-Wave Precision Rectifier

Full-wave precision rectification requires combining half-wave rectification with inversion and summing. One common approach uses two op-amps: a half-wave precision rectifier followed by a summing amplifier that adds the original signal to twice the rectified signal with appropriate polarity.

Alternatively, an absolute value circuit using two op-amps in a different configuration provides full-wave rectification with improved high-frequency response by keeping both op-amps active at all times.

Speed Limitations

When the input crosses zero, the op-amp must transition from one feedback path to another. During this transition, the op-amp may saturate momentarily, causing crossover distortion and limiting maximum operating frequency.

Fast precision rectifiers use techniques to minimize these transitions: keeping the op-amp output from saturating through additional feedback paths, using faster op-amps, or employing synchronous rectification with external switching control.

Applications

• AC voltage measurement: Converting AC signals to DC for measurement
• Peak detection: Capturing signal peaks for envelope detection
• Signal demodulation: Extracting modulation from carrier signals
• Absolute value circuits: Generating |x| function for computation
• Precision AC-DC conversion: Power measurement and control applications

Basic Clamping Operation

A simple diode clamp uses a capacitor to block DC and a diode to establish the reference level. During one half-cycle, the diode conducts, charging the capacitor. During the opposite half-cycle, the diode is reverse-biased, and the charged capacitor adds its voltage to the input signal, shifting the entire waveform.

Passive diode clamps suffer from the diode's forward voltage drop and require multiple time constants to stabilize. The output level drifts as the capacitor slowly discharges through the load or leakage paths.

Precision Clamping with Op-Amps

Placing the diode within an op-amp feedback loop eliminates the forward voltage drop, enabling precision clamping of small signals. The op-amp actively drives the capacitor charging, reducing settling time and improving level accuracy.

The reference voltage for the clamp level can be any value within the op-amp's output range, providing flexible level shifting. Changing the diode orientation changes whether positive or negative peaks are clamped to the reference.

Applications

• DC restoration: Restoring DC level lost through AC coupling
• Video signal processing: Black level clamping in video circuits
• Radar and pulse systems: Baseline restoration for pulse detection
• Level shifting: Repositioning signals for subsequent processing stages
• Peak-to-peak detection: Combined with peak detectors for amplitude measurement

Component Selection

Resistor selection significantly impacts circuit performance. Metal film resistors offer better temperature coefficients and lower noise than carbon composition types. For precision applications, resistor tolerance of 0.1% or better may be necessary, particularly in difference amplifiers and instrumentation amplifiers where matching affects CMRR.

Capacitors in AC-coupled circuits and compensation networks should be film types rather than ceramic for critical applications. Ceramic capacitors (except C0G/NP0 types) exhibit voltage coefficients and microphonic effects that can introduce distortion.

Layout Considerations

Power supply bypassing close to the op-amp power pins is essential for high-frequency performance and stability. Typically, 0.1 microfarad ceramic capacitors should connect within a few millimeters of each power pin.

Signal routing should keep input traces short and away from output traces to minimize crosstalk and oscillation risks. Ground planes help shield sensitive signals but can add capacitance that affects high-frequency response.

Testing and Troubleshooting

When circuits malfunction, first verify power supply voltages at the op-amp pins. Then check that inputs are within common-mode range and that the output is not saturated against a supply rail. For oscillating circuits, check power supply bypassing, probe without adding excessive capacitive load, and consider whether the op-amp is stable with the feedback network and load present.