Introduction to biasing

In the previous sections we have discussed under which conditions a nonlinear resistive element can be used as an amplifying device. First of all, there needs to be an operating point at which the available power of a signal source can be increased. Secondly, we must apply bias voltage and current sources that let the device operate at such an operating point. In order not to adversely affect the signal processing, we may place only ideal voltage sources in series with the signal path and ideal current sources in parallel with the signal path.

However, the bias sources to be applied cannot be chosen freely. For a two-terminal element we may assign an arbitrary value to either the voltage source or the current source. The other one relates to the selected one through the element’s \(v-i\) relation. In general, in a resistive network with \(n\) terminals we may define \(n-1\) bias sources freely while the values of another \(n-1\) bias sources relate to ones selected.

In practice, we will also have to face numerous implementation difficulties. Even if we carefully select the desired operating point and design the required bias sources, the device tolerances as well as temperature dependency of the device characteristics cause temperature-dependent biasing errors that may be too large to maintain the proper operating conditions.

Another practical limitation is imposed by the requirement of a single power supply source. All bias voltage and current sources should in some way be derived from a single source or a limited number of power sources. If we have multiple sources at our disposal, these sources usually share a common terminal. This will impose serious limitations to the implementation of floating bias sources.

In this section we will only give a brief introduction to biasing and not addresses all these topics. A more detailed treatment of biasing will be given in Chapter Amplifier Biasing.

Independent and dependent bias sources

In the introduction we have already stated that not all operating point variables can be chosen independently. The first question we need to answer is which one(s) do we want to fix by design and which one(s) as dependent variable(s). To this end, let us consider a biased two-port with amplifying capabilities. Such a two-port will exhibit a large available power gain if its transmission-1 small-signal parameters in the operating point are close to zero. This can be seen from ((11)). In such cases, the voltage and current excursions at the output port exceed those at the input port. If we take the input bias quantities as independent and fixed, then the output bias current and bias voltage will depend on the device characteristics and on the temperature. In order to prevent from clipping during large signal excursions at the output port, we may need to apply much larger bias sources than strictly required on grounds of the signal handling requirements. This is because we have to account for device tolerances and temperature changes. Hence, it will be clear that selecting the output port bias quantities on grounds of the signal handling requirements, while adapting the values of the input bias sources to device tolerances and temperature changes, will result in a better power efficiency. Moreover, in later chapters we will see that many performance aspects, such as the noise behavior, the bandwidth and the linearity of biased amplifying devices show a direct relation with the operating voltage and current of the output port.

Biasing of 3-terminal elements

Amplifying devices such as MOSFETs, JFETs and BJTs can be used as 3-terminal active devices. Operation and modeling of these devices will be discussed in Chapter Active Devices. Here, we will discuss generalized biasing methods for these devices.

Fig. 67 A nonlinear two-port with its output port biased at \(\left (V_O,I_O\right)\). In order to achieve zero load voltage and current at a given temperature, the input port needs to be biased at \(\left (V_I,I_I\right)\).

Let us assume that a passive nonlinear resistive 3-terminal element can deliver a sufficiently large load signal if its output port is biased at a voltage of \(V_{O}\) and at a current \(I_{O}\). Let us also assume that, at a given temperature, the biasing of its output port requires a bias voltage \(V_{I}\) and a bias current \(I_{I}\) at its input port. This situation is shown in Fig. 67.

The question is how to obtain the required values of the input port bias quantities \(V_{I}\) and \(I_{I}\). One way is to use the device equations and obtain analytical expressions for the input port quantities. With strongly simplified device equations this may yield useful estimations for taking early stage design decisions.

Fig. 68 Determination of the input port biasing quantities \(\left (V_I,I_I\right)\) with the aid of a nullor.

If we want to create an accurately biased two-port that can be used during simulation, we can use the approach sketched in Fig. 68. In this configuration a nullator sets the zero load condition and the norator provides \(\left( V_{I},I_{I}\right) \) that satisfies this condition. Such a setup works if this network has a unique DC solution at the temperature of interest. This will usually be the case with amplifier stages. If not, \(\left( V_{I},I_{I}\right) \) should be limited to a range in which a unique solution exists.

Fig. 69 Biased 3-terminal element.

Fig. 69 shows the biasing result. A bias current source and a bias voltage source are connected to the input port to create zero load conditions for all passive, DC port terminations, while having its output port biased at \(\left( V_{O},I_{IO}\right) \).

Amplification mechanism

Fig. 70A shows an amplifier stage with a biased 3-terminal element, driven from a voltage source with a finite, nonzero source resistance. The stage is biased as described in section Biasing of 3-terminal elements. We assume positive nonzero values for all the bias sources. In Chapter Active Devices we will see that the commonly used (N-type) amplifying devices require such biasing conditions. The amplification mechanism is explained in the caption of this figure.

Fig. 70 Voltage-driven amplifier stage with the three terminal, passive, resistive element, which is biased according to Figure {Fig. 69}.

A: Biased 3-terminal element in the quiescent state. For proper operation of this device, all bias voltages and currents are positive (NMOS, NPN, vavuum tube).

B: Sink state: the stage is driven from a positive voltage. The output current of the 3-terminal device increases. The extra (sink) current is delivered by the output bias voltage source. The output voltage of the 3-terminal device drops below \(V_O\) and the load voltage \(v_{\ell}\) drops below zero.

C: Source state: the stage is driven from a negative voltage. The output current of the 3-terminal device decreases. The excess current delivered by the output bias current source flows through the load. The output voltage of the 3-terminal device rises above \(V_O\) and the load voltage \(v_{\ell }\) becomes positive.

D: Compact model of the biased 3-terminal element. This model comprises an active element: a voltage-controlled voltage source. For the sake of simplicity, a possible reverse transfer is not modeled. Under the conditions that no breakdown or saturation effects are present, this stage operates in Class A.

This Fig. 70D shows that a combination of a passive, resistive, three-terminal amplifying device and properly configured bias sources, can be modeled with the aid of a controlled source, which is an active network element since it delivers power to its load.

Deriving the bias sources from the power supply

Fig. 71 \(V-I\) characteristic of a two-terminal resistive elements that exhibits a current source character when biased at a sufficiently large voltage.

The biasing of a 3-terminal element with four bias sources is conceptually correct, but not very practical. Generally we want the amplifier to be supplied from a few power sources that share the reference terminal. This means that the bias voltages and currents in some way have to be derived from the power supply source(s). The general procedure for this is first to minimize the number of bias sources and then derive them from the power supply with passive, (nonlinear) resistive elements. Such elements should exhibit either a voltage source character when operating at a non-zero current, or a current source character when operating at a non-zero voltage.

A two-terminal resistive element exhibits a voltage source character if, at an operating point \((V_Q,I_Q)\), its small-signal resistance is smaller than \(\frac{V_Q}{I_Q}\). A two-terminal resistive element exhibits a current source character if, at an operating point \((V_Q,I_Q)\), its small-signal conductance is smaller than \(\frac{I_Q}{V_Q}\).

For bias voltage sources we will use elements with a voltage-source character and for bias current sources we will use elements with a current source character.

Fig. 71 shows an example of the \(V-I\) characteristic of a nonlinear resistive two-terminal element that exhibits a current source character when biased at a voltage between saturation and breakdown: \(V_{sat}<V<V_{br}\). Outside this range we speak of voltage limiting or clipping.

Chapter Amplifier Biasing is devoted to this topic. There, we will also discuss biasing techniques that use AC coupling. The concept of AC coupling will be introduced in Chapter Introduction to amplifier biasing. A chapter about the design of the bias sources themselves has not yet been included.