E7G: Operational Amplifiers
The operational amplifier (op-amp) is one of the most versatile building blocks in analog electronics. With external feedback components, it can amplify, filter, integrate, differentiate, compare, and perform mathematical operations. Understanding the key characteristics of op-amps and how to calculate gain from external resistors is essential for the Extra class exam.
This lesson covers op-amp characteristics, the inverting amplifier configuration, gain calculations from Figure E7-3, gain-bandwidth product, input offset voltage, active filter design, and preventing instability.
Op-Amp Characteristics
An operational amplifier is a high-gain, direct-coupled differential amplifier with very high input impedance and very low output impedance. These characteristics make it ideal as a building block:
- Input impedance: Very high — the op-amp draws negligible current from the signal source, avoiding loading effects.
- Output impedance: Very low — the op-amp can drive loads without significant voltage drop.
- Open-loop gain: Extremely high (typically 100,000 or more), making it useful for precision applications with feedback.
- Differential input: The op-amp amplifies the difference between two input terminals (inverting − and non-inverting +).
For an ideal op-amp, the open-loop voltage gain does not vary with frequency — it is flat across all frequencies. Real op-amps do have a frequency rolloff, but the ideal model assumes infinite gain-bandwidth.
Inverting Amplifier and Gain
In the inverting amplifier configuration, the input signal is connected through a resistor R1 to the inverting (−) input. A feedback resistor RF connects from the output back to the inverting input. The non-inverting (+) input is connected to ground.
The voltage gain of an inverting amplifier is: Gain = −RF / R1. The negative sign indicates phase inversion — the output is inverted relative to the input. The absolute (magnitude) gain is simply RF / R1.
- R1 = 10 Ω, RF = 470 Ω → Gain = 470/10 = 47
- R1 = 1,800 Ω, RF = 68,000 Ω → Gain = 68000/1800 ≈ 38
- R1 = 3,300 Ω, RF = 47,000 Ω → Gain = 47000/3300 ≈ 14
- R1 = 1,000 Ω, RF = 10,000 Ω, Vin = 0.23 V → Vout = −(10/1) × 0.23 = −2.3 V
Gain-Bandwidth Product
The gain-bandwidth product of an op-amp is the frequency at which the open-loop gain of the amplifier falls to one (unity gain). It is a constant for a given op-amp: if you increase closed-loop gain, the usable bandwidth decreases proportionally, and vice versa.
For example, if an op-amp has a gain-bandwidth product of 1 MHz, a closed-loop gain of 100 is only achievable up to about 10 kHz; at 100 kHz, the maximum gain is about 10. This trade-off must be considered when designing high-gain, wide-bandwidth circuits.
Input Offset Voltage
Input offset voltage is the differential input voltage that must be applied to bring the open-loop output voltage to zero. In an ideal op-amp, zero differential input would produce zero output. In a real op-amp, a small offset voltage at the input causes a large output voltage (amplified by the open-loop gain). Precision applications require op-amps with low offset voltage specifications.
Active Filters with Op-Amps
Adding capacitors to the feedback or input network of an op-amp creates frequency-dependent gain — an active filter. When a capacitor is added across the feedback resistor RF, the feedback impedance decreases at higher frequencies (because capacitive reactance decreases with frequency). This reduces the gain at higher frequencies while leaving low-frequency gain unchanged, creating a low-pass filter response.
Preventing Instability
Op-amp audio filters can develop unwanted ringing — oscillation at or near the filter's resonant frequency — if gain and Q are too high. To prevent unwanted ringing and audio instability in an op-amp audio filter, both gain and Q must be restricted. Increasing either one without limit allows the filter to approach oscillation. Keeping both parameters within bounds ensures a stable, well-damped filter response.
Figure E7-3: Inverting Amplifier Calculations
Figure E7-3 shows a standard inverting op-amp amplifier circuit. Five exam questions ask about the gain and output voltage of this circuit for different values of R1 and RF.
The formula to remember: |Gain| = RF / R1. For output voltage: Vout = −(RF / R1) × Vin.
If a capacitor is added across RF in this circuit, the result is a low-pass filter — gain drops at frequencies where the capacitor's reactance becomes significant relative to RF.
E7G Practice Questions
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