Basic techniques

In this section, we will discuss basic biasing techniques. First, we will discuss the concept of biasing with level shifts and bias current sources. Then, we will discuss implementations with AC coupling.

Basic biasing technique

The application of level shifts and bias currents has already been introduced in section Modeling of the static nonlinear behavior. In Fig. 50, we shifted the quiescent operating point of the amplifier from \((V_{pQ},~I_{pQ})\) to \((0,~0)\) by placing a bias voltage source \(V_{pQ}\) in series with the amplifier port and a bias current source \(I_{pQ}\) in parallel with the amplifier port. This method can be applied at the input port of the amplifier and at the output port of the amplifier. In the following example, we will design the biasing concept of the amplifier from fig-micAmpADCsystem using bias current sources and voltage level shifts.

Example

Fig. 295 Concept design of the amplifier from fig-micAmpADCsystem .

Let us assume we have designed the amplifier from fig-micAmpADCsystem as a passive feedback voltage amplifier with a voltage gain of \(20\). Fig. 295 shows the concept of this amplifier. The source quantity is the one that has the best reproducing relation with the primary information (sound pressure), and the impedance of this source is the small-signal source impedance. Here, the voltage source \(V_{s}\) and its source impedance \(Z_{s}\) represent the microphone. The input impedance of the ADC is the load impedance\(\ Z_{\ell}\) of the amplifier. During the conceptual design of the amplifier, we do not consider the biasing and the power supplies. The amplifier is simply assumed to behave as a linear two-port that has the \(v-i\) characteristics of both ports passing through the origin. The ground node is the power supply reference node.

Fig. 296 shows the amplifier in which the controller has been implemented with an operational amplifier and to which bias sources have been added.

Fig. 296 Implementation of the controller with an operational amplifier and biasing concept of the amplifier from Fig. 295.

We start the design of the biasing by choosing the power supply voltages of the operational amplifier such that it can drive the load with \(\pm2\)V signal excursion. Fig. 296 shows these power supply voltages \(V_{P}\) and \(V_{N}\) for the positive power supply and the negative power supply, respectively.

Then, the operating point of the source and the load will be modeled. The \(2\)V bias voltage of the ADC and the bias current of the ADC have been modeled with \(V_{\ell Q}\) and \(I_{\ell Q}\), respectively. The signal source should operate at zero bias, which requires no additional bias sources.

We then start with the design of the biasing of the amplifier. The output voltage range of the amplifier is adjusted to \(0\cdots4\)V by adding an output offset voltage \(V_{O}=2\)V to the output voltage of the amplifier. This is done by inserting a \(2\)V voltage source between the output of the amplifier and the input of the ADC. The bias current of the ADC is compensated for by an equally large current source in parallel with the output port of the amplifier. The input bias currents \(I_{iQ}\) of the operational amplifier have been compensated for by two current sources with a value \(I_{iQ}\). In this way, both the input port and the output port of the amplifier operate at zero bias: the \(v-i\) characteristics of both amplifier ports pass through the origin.

For the sake of simplicity, we assumed zero equivalent input offset voltage and zero equivalent offset current for the operational amplifier.

Hence, at zero signal voltage, the source impedance, the load impedance, the amplifier input port, its feedback network and its output port all carry no current.

Before we will find a practical implementation for the biasing concept from Fig. 296, we will introduce the terms DC coupling and AC coupling.

DC coupling and AC coupling

DC coupling

We speak of DC coupling between a source and a load if there is a nonzero DC transfer from the source to that load. If there exists only a nonzero transfer for frequencies that differ from zero, we speak of AC coupling.

Fig. 297A shows two disconnected networks. There is no transfer from the source current \(I_{s}\) to the load voltage \(V_{\ell}\). Fig. 297B shows the two networks connected through a resistive branch. However, there is still no transfer from the source to the load. Fig. 297C shows the two networks connected through two resistive branches. Now there exists a DC coupling from the source to the load because there is a nonzero DC transfer from \(I_{s}\) to \(V_{\ell}\). Fig. 297D shows the two networks connected through one resistive and one capacitive branch. In this case, there exists a nonzero transfer only for frequencies that differ from zero, hence we have an AC coupling between the source and the load.

Fig. 297 Coupling between networks: A: Two disconnected networks B: The two networks are connected, but there exists no transfer between the two networks C: The two networks are connected and there exists a nonzero DC transfer from the left network to the one on the right D: The two networks are connected, but there exists only a nonzero AC transfer between the two networks.

AC coupling

Two networks are AC coupled if there only exists a transfer from one network to the other network for frequencies that differ from zero. Hence, a change in the DC operating point of a network that has an AC coupling with another network, does not cause a change the of the DC operating point of this other network. The following rules apply to AC coupling :

1. AC coupling can be applied if signal components with very low frequencies are not of interest to the observer.

2. AC coupling between a source or a detector and an amplifier has to be applied if bias currents or bias voltages of the amplifier ports are not allowed to appear at the source or at the load.

3. AC coupling between two networks can be established by creating a high-pass transfer between the two networks.

4. If a nonzero DC transfer has to be established, but errors due to bias quantities are too large, the frequency range of the information needs to be changed such that DC transfer is no longer required. This principle of modulation and demodulation is applied in so-called chopper amplifiers.

Deriving bias quantities from the power supply

There exist many different implementations of the biasing of the amplifier from fig-micAmpADCsystem. In the following example, we will design a biasing scheme with DC coupling between the amplifier and the ADC and AC coupling between the signal source and the amplifier.

Example

Fig. 298 Amplifier from Fig. 296 with \(2\)V added to all nodal voltages.

In this example, we will implement the biasing of the amplifier from fig-micAmpADCsystem without the need for a level shift between the output of the amplifier and the ADC. We will start with the elimination of the \(2\)V voltage source between the output of the amplifier and the input of the ADC.

This is because accurate low-noise voltage sources that are floating with respect to the ground, are hard to realize.

To this end, we increase the DC level of all the nodal voltages of the amplifier with \(2\)V. Fig. 298 shows the way in which this is done. Please notice that at the quiescent operating point, all voltage sources except the power supply voltage sources do not carry DC current! This is because all the required DC bias currents have been provided by DC current sources.

Since the frequency contents of the signal does not include DC, AC coupling may be applied. With AC coupling, level shifts that do not carry DC currents may be replaced with capacitors. These capacitors introduce impedances in series with the signal path. These impedances must be small enough not to deteriorate the signal-to-noise ratio and the power efficiency of the amplifier. This has to be the case at all frequencies of interest.

Fig. 299 shows the result of this AC coupling. The capacitors \(C_{1}\) and \(C_{2}\) can be considered as small batteries implementing \(V_{1}\) and \(V_{2}\) from Fig. 298, respectively. The DC voltage across these capacitors equals \(2\)V.

Fig. 299 Amplifier from Fig. 298 with the level shifts V1 and V2 replaced with capacitors.

In practice, the biasing scheme shown in Fig. 299 will not provide a stable and well-defined biasing. This is because the bias currents of the operational amplifier are usually inaccurately known and strongly depend on temperature. In addition, the input impedance of the voltage amplifier is very high. These two properties result in a very badly defined DC voltage at the input of the amplifier, and measures have to be taken to convert this theoretically correct bias solution into a working one.

This can be seen as follows: The common-mode input bias voltage error is the product of the common-mode input resistance and the error in the common-mode bias current. Operational amplifiers usually exhibit a very high input common-mode resistance, an inaccurately defined input bias current and a high relative input-bias current drift. The product of their common-mode input resistance and the unpredictable part of the bias current almost always exceeds the input common-mode voltage range.

For a complete design, we need to:

1. Determine the power supply voltages

   The minimum value of \(V_{P}\) equals the positive peak value of the output voltage plus the maximum value of the voltage drop in the output stage of the operational amplifier. This voltage drop depends on the internal structure of the output stage of the operational amplifier, on the temperature and on the current delivered by the amplifier. Fig. 275 shows a plot of the output voltage and current drive capabilities of an operational amplifier.

   The positive voltage headroom is defined as the difference between this minimum required value of \(V_{P}\) and the actual value of \(V_{P}\). The maximum value of \(V_{N}\) is determined in a similar way, now accounting for the negative voltage headroom. A large headroom is usually beneficial to the distortion, but it decreases the power efficiency of the amplifier.

2. Evaluate biasing errors

   Power supply tolerances, device tolerances and both the input offset voltage and the input offset current of the operational amplifier all introduce biasing errors. These errors may result in a reduced or even in a negative headroom.

   A negative headroom occurs if the voltage drive or the current drive capabilities are smaller than required.

   Section Evaluation of biasing errors is devoted to this topic.

3. If necessary, consider the application of error reduction techniques for improvement of the accuracy and the stability of the biasing

   If a certain biasing scheme results in unacceptably large biasing errors, error reduction techniques may be used to improve the biasing accuracy and stability. Application of such techniques will be discussed in section Application of error reduction techniques.

4. Verify the behavior with computer simulations and prototyping

In the following example, we will show a complete bias solution and discuss the above topics qualitatively.

Example

\label{ex-micVampBiasImplemented}

Fig. 300 Amplifier from Fig. 299 with brute-force input biasing and without input bias current and load bias current compensation.

Fig. 300 shows a possible bias solution for the amplifier.

In this example, we use an operational amplifier with a rail-to-rail output stage. The positive and the negative voltage headroom are assumed to be sufficiently large with \(V_{P}=4.5\)V and \(V_{N}=-0.5\)V. In this solution, the common-mode input voltage of the amplifier should at least range from \(1.9\cdots2.1\)V, which is \(2.4\)V below the positive supply and \(2.4\)V above the negative supply voltage.

The resistors \(R_{3}\) and \(R_{4}\) fix the DC voltage at the noninverting input of the amplifier. This way of fixing the voltage at the noninverting input of the operational amplifier is basically a brute-force technique. Care should be taken as to the possible deterioration of the signal-to-noise ratio and the power efficiency of the amplifier. In order to minimize both the noise contribution and its effect on the gain, the linearity and the power supply rejection of the amplifier, the resistance of the parallel connection of \(R_{3}\) and \(R_{4}\) should be as large as possible. However, for a small biasing error, this resistance should be small enough. The biasing errors resulting from the input bias current and the offset current of the amplifier are proportional to \(R_{3} || R_{4}\).

If an operational amplifier with the required common-mode input voltage range cannot be found, there are two options:

1. Increase the supply voltage such that the input common-mode voltage range of the operational amplifier satisfies the requirements.

2. Change the requirement for the common-mode input voltage range of the opamp.

   This can be achieved by changing the values of \(V_{1}\) and \(V_{2}\) in the circuit from Fig. 298. It can be implemented by changing the ratio \(\frac{R_{3}}{R_{4}}\) and by inserting a DC current into the inverting input of the operational amplifier. This DC current is the Norton equivalent of the voltage change in \(V_{2}\) in series with \(R_{1}\). A low-noise implementation of this current source can be made by inserting a resistor \(R_{5}\), as shown in Fig. 300. If the common-mode input voltage must be below the DC output voltage of the operational amplifier, \(R_{5}\) should be connected to the negative supply, and otherwise to the positive supply voltage.

AC decoupling

AC decoupling means minimization of an AC transfer , while maintaining a DC transfer. It is the opposite of AC coupling ; it requires a low-pass filter action instead of a high-pass one. In example ex-micVampBiasImplemented, the resistor \(R_{5}\) connects the signal path of the amplifier to the power supply voltage. The capacitor \(C_{2}\) performs two functions:

1. It acts as an AC coupling capacitor , because it establishes a high-pass character of the voltage amplifier

2. It acts as an AC decoupling capacitor , because it establishes a low-pass character in the voltage transfer from the power supply to the output.

In fact, the above can also be said for \(C_{1}\) in combination with \(R_{3}\) and \(R_{4}\). However, the effectiveness of the AC decoupling by \(C_{1}\) is limited by \(Z_{s}\). At signal frequencies of interest, \(C_{1}\) should act as a short with respect to \(Z_{s}\), and at those frequencies, the transfer from the power supply voltages to the noninverting input of the operational amplifier will only be small if \(\left\vert Z_{s}\right\vert \ll R_{3} || R_{4}\).

Fig. 301 Amplifier from Fig. 300 with a larger PSRR due to improvement of the power supply decoupling.

Fig. 301 shows an arrangement for the amplifier with an improved PSRR in which extra power supply decoupling has been implemented with \(C_{3}\). The power supplies, together with \(R_{3}\), \(R_{4}\) and \(C_{3}\), constitute a low noise, low impedance voltage reference. The resistor \(R_{6}\) connects the noninverting input of the operational amplifier to this reference, while maintaining a high input impedance for the voltage amplifier, just as \(R_{3}\) and \(R_{4}\) did in the circuit from Fig. 300.