Op-Amp Gain & Bandwidth Calculator
Calculate op-amp voltage gain, gain in dB, −3 dB bandwidth, and input impedance for inverting, non-inverting, and differential amplifier configurations.
Formula
A_v^{non-inv} = 1 + \frac{R_f}{R_{in}}, \quad A_v^{inv} = -\frac{R_f}{R_{in}}, \quad f_{-3dB} = \frac{GBW}{|A_v|}
Reference: Horowitz & Hill, The Art of Electronics, 3rd ed.
How It Works
Operational amplifiers (op-amps) are fundamental building blocks in analog electronics, providing voltage amplification, signal conditioning, and mathematical operations. The gain of an op-amp circuit depends on its configuration and feedback network. In a non-inverting configuration, the input signal is applied to the positive terminal, with negative feedback controlling gain. The gain equation G=1+Rf/Rin reflects how the feedback resistor (Rf) and input resistor (Rin) determine amplification. The inverting configuration applies the input to the negative terminal, creating a 180-degree phase shift in the output. Here, the gain is determined by the ratio -Rf/Rin, with the negative sign indicating phase inversion. Bandwidth is a critical parameter, characterized by the gain-bandwidth product (GBW), which represents the maximum frequency at which the amplifier can maintain a specific gain level. The -3dB frequency (f-3dB) is calculated by dividing the GBW by the absolute gain magnitude, providing insight into the amplifier's frequency response limitations.
Worked Example
Consider an LM358 op-amp in a non-inverting configuration with Rf = 10 kΩ and Rin = 2.2 kΩ. The gain calculation would be G = 1 + (10,000 Ω / 2,200 Ω) = 5.55. This means the input signal will be amplified by a factor of 5.55. If the op-amp has a gain-bandwidth product of 1 MHz, the -3dB frequency would be calculated as 1 MHz / |5.55| ≈ 180 kHz. At this point, the amplifier's output will have dropped by 3 decibels from its nominal gain, indicating the circuit's practical bandwidth limitation.
Practical Tips
- ✓Use decoupling capacitors close to the op-amp power pins to reduce noise
- ✓Select op-amps with gain-bandwidth product well above your design requirements
- ✓Consider input impedance requirements to prevent loading effects
Common Mistakes
- ✗Neglecting the op-amp's real-world limitations like slew rate and input offset voltage
- ✗Assuming infinite bandwidth regardless of gain setting
- ✗Improper PCB layout leading to parasitic capacitance and reduced performance
Frequently Asked Questions
What is the difference between inverting and non-inverting amplifier configurations?
In a non-inverting configuration, the input signal is applied to the positive terminal and the output is in-phase with the input. In an inverting configuration, the input is applied to the negative terminal, causing a 180-degree phase shift.
How does feedback affect op-amp gain?
Feedback resistors determine the gain by creating a ratio that controls the amplification factor. The specific arrangement of these resistors defines the circuit's gain characteristics.
What limits op-amp bandwidth?
The gain-bandwidth product (GBW) is the primary limitation, which represents the maximum frequency at which the amplifier can maintain a specific gain level.
Can an op-amp amplify DC signals?
Most op-amps can amplify DC signals, but practical considerations like input offset and drift must be considered for high-precision DC applications.
How do I choose the right op-amp for my design?
Consider parameters like gain-bandwidth product, slew rate, input impedance, power consumption, and operating voltage range when selecting an op-amp.
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