Operational amplifiers are the backbone of analog circuits, and understanding inverting and non-inverting amplifiers is crucial. These configurations allow us to manipulate signals, providing gain or attenuation as needed in various applications.
Inverting amplifiers flip the input signal, while non-inverting amplifiers maintain its phase. Both types offer unique advantages and limitations, making them suitable for different scenarios. Mastering these concepts is essential for designing effective analog systems.
Inverting Amplifier Circuits
Circuit Configuration and Principles
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Inverting amplifier produces output signal inverted and amplified relative to input signal
Circuit consists of op-amp with negative feedback
Input signal applied to inverting input through resistor
Feedback resistor connects output to inverting input
Non-inverting input typically connected to ground
Virtual ground concept creates ground potential at inverting input due to negative feedback
Closed-loop gain determined by ratio of feedback resistor to input resistor
Gain formula: G a i n = − R f / R i n Gain = -R_f/R_{in} G ain = − R f / R in
Negative sign indicates 180° phase shift between input and output
Input impedance approximately equal to input resistor value
Design Considerations and Analysis
Calculate closed-loop gain using A C L = − R f / R i n A_{CL} = -R_f/R_{in} A C L = − R f / R in
Input impedance Z i n ≈ R i n Z_{in} \approx R_{in} Z in ≈ R in (approximately equal to input resistor)
Output impedance Z o u t ≈ 0 Z_{out} \approx 0 Z o u t ≈ 0 (very low, ideally zero)
Effect of finite open-loop gain on closed-loop gain accuracy
Actual gain = Ideal gain / (1 + Ideal gain/AOL)
AOL represents open-loop gain of op-amp
Bandwidth considerations
Gain-bandwidth product of op-amp limits maximum achievable gain at higher frequencies
Constant bandwidth over wide range of closed-loop gains
Examples:
For R f = 10 k Ω R_f = 10 k\Omega R f = 10 k Ω and R i n = 1 k Ω R_{in} = 1 k\Omega R in = 1 k Ω , gain = -10
Input signal of 0.5V results in -5V output (inverting amplifier with gain of -10)
Non-inverting Amplifier Circuits
Circuit Configuration and Principles
Non-inverting amplifier produces output signal in phase with and amplified relative to input signal
Circuit consists of op-amp with negative feedback
Input signal applied to non-inverting input
Voltage divider feedback network connected between output and inverting input
Inverting input connected to junction of two resistors forming feedback voltage divider
Closed-loop gain determined by ratio of feedback resistors
Gain formula: G a i n = 1 + ( R f / R 1 ) Gain = 1 + (R_f/R_1) G ain = 1 + ( R f / R 1 )
R f R_f R f represents feedback resistor, R 1 R_1 R 1 represents resistor connected to ground
Output signal in phase (0° phase shift) with input signal
Input impedance very high (ideally infinite)
Provides better common-mode rejection compared to inverting configuration
Design Considerations and Analysis
Calculate closed-loop gain using A C L = 1 + ( R f / R 1 ) A_{CL} = 1 + (R_f/R_1) A C L = 1 + ( R f / R 1 )
Input impedance Z i n ≈ ∞ Z_{in} \approx \infty Z in ≈ ∞ (very high, ideally infinite)
Output impedance Z o u t ≈ 0 Z_{out} \approx 0 Z o u t ≈ 0 (very low, ideally zero)
Bandwidth decreases with increasing gain
Minimum gain of unity (cannot attenuate signals without additional circuitry)
More susceptible to input-referred noise at high gains
Examples:
For R f = 9 k Ω R_f = 9 k\Omega R f = 9 k Ω and R 1 = 1 k Ω R_1 = 1 k\Omega R 1 = 1 k Ω , gain = 10
Input signal of 0.5V results in 5V output (non-inverting amplifier with gain of 10)
Amplifier Characteristics
Closed-loop gain accuracy dependent on resistor tolerances and op-amp open-loop gain
Slew rate limits large-signal performance
Affects maximum rate of change of output voltage
Example: Slew rate of 10 V/μs limits 1 MHz sine wave to 10 Vpp amplitude
Output voltage swing limited by op-amp power supply voltages and saturation characteristics
Example: ±15V supply typically allows ±13V output swing
Common-mode rejection ratio (CMRR) measures ability to reject common-mode signals
Non-inverting configuration generally provides better CMRR
Gain-bandwidth product (GBP) determines maximum achievable gain at specific frequencies
Example: Op-amp with 1 MHz GBP can achieve gain of 10 up to 100 kHz
Impedance Considerations
Inverting amplifier input impedance approximately equal to input resistor value
Can be a disadvantage in some applications due to loading effects
Example: 1 kΩ input resistor results in 1 kΩ input impedance
Non-inverting amplifier input impedance very high (ideally infinite)
Minimizes loading effects on input source
Advantageous in applications requiring minimal source loading
Example: Input impedance >1 MΩ common in non-inverting configurations
Output impedance for both configurations very low (ideally zero)
Allows driving of various loads with minimal effect on output voltage
Example: Typical output impedance <100 Ω
Inverting vs Non-inverting Amplifiers
Comparative Advantages
Inverting amplifier advantages
Achieves gains less than unity (attenuation) without additional components
Example: Gain of 0.5 with R f = 5 k Ω R_f = 5 k\Omega R f = 5 k Ω and R i n = 10 k Ω R_{in} = 10 k\Omega R in = 10 k Ω
Easier implementation of summing amplifier configurations
Example: Multiple inputs summed through separate input resistors
Constant bandwidth over wide range of closed-loop gains
Non-inverting amplifier advantages
Very high input impedance minimizes loading effects on input source
Example: Input impedance >10 MΩ common in many designs
Non-inverted output signal maintains phase relationship with input
Better common-mode rejection ratio compared to inverting configuration
Example: CMRR of 100 dB possible in well-designed non-inverting amplifiers
Comparative Limitations
Inverting amplifier limitations
Lower input impedance compared to non-inverting configuration
Example: 1 kΩ input impedance vs. >1 MΩ for non-inverting
Inverted output signal may be undesirable in some applications
Example: Phase-sensitive demodulation circuits may require non-inverted signal
Potential for increased noise due to virtual ground at inverting input
Non-inverting amplifier limitations
Minimum gain of unity (cannot attenuate signals without additional circuitry)
Bandwidth decreases with increasing gain
Example: Gain of 100 reduces bandwidth to 1% of op-amp's unity-gain bandwidth
More susceptible to input-referred noise at high gains
Example: Noise gain increases proportionally with signal gain