Real operational amplifiers
1. Limitations of real operational amplifiers:
- Real operational amplifiers (op-amps) have several limitations that differ from ideal op-amps:
- – Finite gain: Real op-amps have a finite gain, typically in the range of to 10^6, whereas ideal op-amps have infinite gain.
- – Bandwidth: Real op-amps have a limited bandwidth, meaning they can’t amplify signals at very high frequencies.
- – Input offset voltage: Real op-amps have a small voltage difference between the inputs, known as input offset voltage.
- – Input bias current: Real op-amps have a small current flowing into the inputs, known as input bias current.
- – Output voltage swing: Real op-amps have a limited output voltage range.
- – Slew rate: Real op-amps have a limited rate of change of output voltage.
- – Noise: Real op-amps introduce noise into the circuit.
- – Finite input impedance: Real op-amps have a finite input impedance.
- – Finite output impedance: Real op-amps have a finite output impedance.
- – Temperature dependence: Real op-amps are affected by temperature changes.
- – Power consumption: Real op-amps consume power.
- – Non-linearity: Real op-amps exhibit non-linear behavior.
- These limitations affect the performance of op-amp circuits and must be considered in circuit design.
- The table below shows a comparison between a typical and ideal op-amp, noting that the real values will vary for different op-amps.
- Table 1 a comparison between a typical and ideal op-amp
-
Ideal Real Open-loop gain ([math] A_{OL} [/math]) Infinite [math] 10^6[/math] Input resistance ([math] R_{in} [/math]) Infinite – draws on current [math] 10^{12}[/math] Output resistance ([math] R_{out} [/math]) Zero [math] 100Ω[/math] Output voltage ([math] V_{out} [/math]) [math]
-V_s ≤ V_{out} ≤ + V_s[/math][math]
-V_s < V_{out} + V_s, V_{out} ≠ 0 [/math]Bandwidth Infinite – can operate at any input frequency Open-loop – Around 15 Hz Closed-loop – Around 2.5 MHz - A practical op-amp will produce a little voltage known as the off-set voltage when the inverting and non-inverting terminals are the same or both grounded, although an ideal op-amp would produce 0 V.
- Many applications require this value to be cancelled out in order for the op-amp to function properly.
- To achieve this, connect the op-amp to an external voltage divider circuit (designated offset null in the picture below).
- Additionally, because of circuit resistance, a true op-amp is unable to generate precise positive or negative supply voltage values.
-
Figure 1 The pin connections for one type of op-amp
- Because of its high gain, the op-amp’s bandwidth—the range of frequencies at which it operates—is extremely limited in open-loop circuits. Data sheets often quote the closed-loop bandwidth, which is achieved by using an amplifier circuit with unity gain. This allows for a higher bandwidth, but the gain is reduced.
2. Frequency response curve:
- A frequency response curve illustrates how an op-amp’s voltage gain changes in relation to the input signal’s frequency. An open-loop circuit’s frequency response curve is shown in the example below.
- The huge levels of frequency and gain may cause frequency response curves to have a logarithmic scale.
- Figure 2 Frequency response curve
- A frequency response curve is a graph that shows how a system or device responds to different frequencies. In the context of operational amplifiers (op-amps), it’s a plot of the op-amp’s gain versus frequency.
- A typical frequency response curve for an op-amp might look like this:
- – Low-frequency region: The gain is relatively flat and constant (e.g., 0-100 Hz)
- – Mid-frequency region: The gain starts to roll off (decrease) as frequency increases (e.g., 100 Hz-10 kHz)
- – High-frequency region: The gain decreases significantly as frequency increases (e.g., 10 kHz-1 MHz)
- The frequency response curve is important because it shows:
- – Bandwidth: The range of frequencies where the op-amp gain is relatively constant.
- – Cutoff frequency: The frequency where the gain starts to roll off.
- – Gain peaking: A peak in the gain at a specific frequency.
- – Phase shift: A change in the phase of the output signal relative to the input signal.
- Understanding the frequency response curve is crucial for designing and analyzing op-amp circuits, especially in applications like filters, amplifiers, and oscillators.
- This frequency response curve shows that if this op-amp was used as a comparator in an open-loop circuit, its performance will decrease beyond the break frequency, which limits its use. Below is a frequency response curve for the same op-amp but in a closed loop circuit.
- Figure 3 Frequency response curve as a comparator in an open loop circuit
- The frequency response curve in a closed-loop circuit:
- – Gain vs. frequency: The gain of the closed-loop circuit versus frequency.
- – Bandwidth: The range of frequencies where the gain is relatively constant.
- – Cutoff frequency: The frequency where the gain starts to roll off.
- – Gain peaking: Any peaks in the gain response.
- – Phase margin: The difference between the phase shift and -180 degrees.
- – Stability: The circuit’s stability is determined by the phase margin and gain margin.
- – Feedback effects: The feedback network affects the frequency response, gain, and stability.
- In a closed-loop circuit, the op-amp’s open-loop gain and feedback network interact to shape the frequency response. The feedback network can:
- – Reduce gain: Lower the overall gain.
- – Increase bandwidth: Widen the bandwidth.
- – Improve stability: Enhance stability by reducing phase shift.
- – Introduce phase shift: Add phase shift, potentially affecting stability.
- By analyzing the frequency response curve in a closed-loop circuit, you can:
- – Optimize gain and bandwidth.
- – Ensure stability.
- – Determine suitable op-amps.
- – Design appropriate feedback networks.
- As seen in both frequency response curves, beyond the break frequency, the curve approximates a straight line.
- This means that the relationship between voltage gain and bandwidth is linear, meaning that the product of voltage gain and bandwidth must be constant for a given op-amp.
- The relationship defined above can be used to predict the bandwidth of a circuit and is summarized below:
- [math]\text{gain} × \text{bandwidth} = \text{constant}[/math]