In Module 10
Introduction, structure and function of operational amplifiers
Modelling and characteristic variables
Principle of negative feedbackModelling and characteristic variables
The simplified circuit diagram in the previous chapter is well suited for illustrating the internal functioning, but is unsuitable for representation in larger circuits. To make circuit diagrams clearer, operational amplifiers are usually represented by a standard symbol. The internal structure of the amplifier is neglected and characteristic properties are assigned to this general amplifier. Similar to the transistor symbol, the operational amplifier can thus be represented in a simplified form in a circuit.
The following skills are to be acquired within the scope of this chapter:
Learning objectives: Operationsverstärker
The students can
- Describe the differences between the simplified operational amplifier model and real operational amplifiers.
- Specify important areas of the operational amplifier characteristic curve.
The circuit element in Figure 1 (left) shows the inverting input, the non-inverting input, the output, the ground reference and the connections for the supply voltages. This circuit symbol is often found in Anglo-American countries and older documents and is only included here for the sake of completeness. The new circuit symbol (right) should be used in this document. If the reference ground is not explicitly shown, this representation assumes that the output is referenced to ground. For didactic reasons, however, the supply voltages are also specified in this document. The ideal amplifier also has the infinity symbol in the upper right corner. This means that the gain is not limited. The advantage of this circuit element is that amplifiers with amplifier limitations can also be modelled. In this case, the symbol for ‘infinity’ \(\widehat {=}~\infty \) is replaced by a finite value.
Two of the four connections1 of the amplifier, also known as poles, can be combined under idealised conditions to form a so-called „gate“. The operational amplifier can thus be modelled using a so-called two-port model. This is characterised by the fact that, in simplified terms, it can be assumed that the transfer behaviour can be described entirely by the variables current and voltage. The simplification provided by the two-port model means that the internal structure of the operational amplifier can be neglected and regarded as a ‘black box’. The previously rather complicated internal wiring of the transistors can be modelled by the component shown in Figure 1. In addition, the two-port model assumes that no current flows into the inputs of the operational amplifier 2. The following table lists additional properties that facilitate calculations with operational amplifiers. The table also shows classic values for a real operational amplifier, which may vary slightly depending on the amplifier type and are only intended to illustrate the limitations of the two-terminal model.
| Designation | Ideal OPV properties | Typical values (e.g. OPA 121) | Explanation |
| Open-circuit gain | \(V_{\textnormal {Leer}} = \infty \) | \(V_{\textnormal {Leer}} = 10^6\) | Amplification of the voltage present between the inputs when the OPV is not connected. |
| Input impedance | \(Z_{\textnormal {i}} = \infty \) Ω | \(Z_i\) = \(10^{13}\) Ω | The load resistance of the OPV as seen from the source. |
| Output impedance | \(Z_{\textnormal {a}} = 0\) Ω | \(Z_{\textnormal {a}} =~50\) up to \(100\) Ω | The resistance at the output of the OPV as seen from a load. |
| Bandwidth | \(B = \infty \) MHz | \(B >\) 2 MHz | Frequency range in which the amplifier behaviour corresponds to the behaviour specified in the data sheet. |
| Phase shift | \(\varphi \) = 0° | \(\varphi >\) 0° | Delay of the output signal relative to the input signal. |
| Slew Rate | \(\infty \) V | 2 mV bis 1000 V/\(\mu \)s | Maximum voltage increase per unit of time. |
| Output controllability | \(\infty \) | limited to max. \(U_{\textnormal {B}}\) | Maximum output voltage value. |
| Input quiescent current | \(I_{\textnormal {Ruhe}}\) = 0 pA | \(I_{\textnormal {Ruhe}} <\) 5 pA | Input current consumption at differential voltage \(\Delta U_{\textnormal {Diff}}\) = 0. |
| Input offset current | \(I_{\textnormal {Off}}\) = 0 pA | \(I_{\textnormal {Off}} < I_+-I_-\) | Difference between the two input quiescent currents |
| Input offset voltage | \(U_{\textnormal {Off}}\) = 0 mV | \(U_{\textnormal {Off}} < \) 2 mV | Output DC voltage at \(\Delta U_{\textnormal {Diff}}\) = 0 |
| Common mode - Rejection | \(CMR = \infty \) dB | \(CMR\) = 86 dB | Indicates how well the amplifier suppresses signals that are equally present at both inputs. |
The characteristic curve of an operational amplifier can be constructed using the information provided above. This is shown in the following figure:
Figure 2 shows the horizontal shift of the amplifier characteristic curve resulting from the offset voltage \(U_{\text {Off}}\). It can also be seen that the amplifier exhibits linear amplification behaviour with respect to the applied input voltage within its specified operating range (shown in green). The slope in the linear range depends on the maximum amplification of the operational amplifier used. If this specified operating range is exceeded, the output voltage initially exhibits a non-linear relationship to the input voltage (shown in yellow). However, the output voltage continues to rise until saturation is reached. In the area marked in red, the output voltage remains constant even if the input differential voltage continues to increase. As long as the output voltage is within the operating range of the operational amplifier, a constantly amplified output voltage with an offset is output. The actual achievable output voltage is specified by the variable „Output Voltage Swing“. The difference to the positive or negative supply voltage (\(+U_{\textnormal {B}}\) and \(-U_{\textnormal {B}}\)) is referred to as „Headroom“. The headroom is the result of a PN junction in the semiconductor components used in the operational amplifier and is therefore usually 0.6 - 0.7 V. Headroom is an important parameter for the design of operational amplifiers. Operational amplifiers with very low headroom are usually classified by manufacturers as „rail-to-rail“ amplifiers.
Key point:
To simplify calculations with operational amplifiers, a simplified model is often used. It is important to be aware of the limitations of this model and to take them into account when selecting components and designing circuits.
