Nonenergic feedback

Nonenergic negative feedback amplifiers have feedback networks that solely consist of nonenergic network elements. Nonenergic network elements have no energy storage and do not dissipate power; they are instantaneous and noise-free. It will be shown that the noise performance and the power efficiency of nonenergic feedback amplifiers are not affected by their feedback networks as it will be with passive feedback amplifiers.

The following network elements are nonenergic:

1. Short circuit (one port, \(V=0,~\)for all values of\(~I\))

2. Open circuit (one port, \(I=0,~\)for all values of\(~V\))

3. Ideal transformer (two port, \(A=\frac{1}{n},\) \(B=0,\) \(C=0,\) \(D=n)\)

4. Ideal gyrator (two-port, \(A=0,\) \(B=\frac{1}{G},\) \(C=G,\) \(D=0\)).

Design of nonenergic amplifier configurations

All amplifier configurations with floating or grounded ports, having either inverting or noninverting transfer, can be designed as nonenergic feedback amplifiers, using ideal transformers and gyrators feedback elements. A nonenergic feedback voltage amplifier has already been shown in Fig. 215G. In the following example, we will demonstrate the design of a dual-loop negative feedback amplifier.

Example

Fig. 223 Two nonenergic feedback loops around a nullor that fix \(A\) and \(C\) independently.

We will design a negative feedback amplifier that has zero output im - pedance and its input impedance accurately fixed to a nonzero value. Let us first study the expressions for the input and the output impedance of an amplifier ((4)) and ((5)), respectively. From these expression, we can conclude that we need to fix the transmission-1 parameters \(A\) and \(C\) to a nonzero value and have \(B=D=0\). The amplifier will then have \(Z_{i}=A/C\) and a voltage gain factor \(V_{o}/V_{i}=1/A\). If we want to fix \(A\) with the aid of nonenergic negative feedback, we need to sense the output voltage \(V_{o}\) and compare it with the input voltage \(V_{i}\), thereby using a nonenergic feedback element. A nonenergic voltage-to-voltage converter is a transformer. If we want to fix \(C\) with the aid of nonenergic negative feedback, we need to sense \(V_{o}\), convert it into a current and subtract that current from \(I_{i}\). A gyrator can be used for this purpose. If we combine both feedback loops, we obtain the circuit depicted in Fig. 223. It has: \(A=1/n\), \(B=0\), \(C=G\), and \(D=0\).

In the next example, we will add a third loop to fix \(D\) of this amplifier.

Example

Fig. 224 Three nonenergic feedback loops around a nullor that fix \(A\) , \(C\) and \(D\) independently.

If we also want to fix \(D\), we need to sense the output current of the amplifier. If we do this without changing the sensing conditions for the voltage-sensing elements, the third loop will not change the values of the previously designed parameters \(A\) and \(C\). Fig. 224 shows a solution in which a second transformer is used to sense the output current and subtract an attenuated copy of it from the input current. The voltage drop across this transformer has been kept zero by placing its port for the input current comparison in parallel with the nullator. Now, the current through the voltage-sensing transformer T1 is not longer zero, but this does not affect the voltage sensing. Hence, the circuit from Fig. 224 has: \(A=1/n_{1}\), \(B=0\), \(C=G\) and \(D=n_{2}\).

Fig. 225 (A) Non-energic voltage follower and (B) nonenergic current follower.

A fourth feedback loop can be added to fix the parameter \(B\) as well. This would require a second gyrator that converts the output current into a voltage and subtracts that voltage from the input voltage. If we were to place one port of the gyrator in series with the output of the amplifier and the other one in series with the input, while maintaining zero current through the voltage comparison port of this gyrator, it would fix the amplifier’s transmission-1 parameter \(B\) without affecting the other parameters. Unfortunately, such an arrangement is not possible. Adding this gyrator would also affect the other transmission-1 parameters of the amplifier. This was demonstrated by Nordholt[6].

All \(16\) amplifier configurations listed in Table 19 can be obtained with the aid of negative feedback. One loop fixes one parameter only, if the voltage sensing and current sensing of the feedback elements can be realized independently, as demonstrated in the examples above.

Short circuits and open circuits are also nonenergic elements. The unity-gain voltage amplifier and the unity-gain current amplifier, as shown in Fig. 225, use short circuits in series with the signal path and open circuits in parallel with the signal path as feedback elements. Hence, these amplifiers belong to the class of nonenergic feedback amplifiers.

Noise behavior of nonenergic feedback amplifiers

Fig. 226 shows a nonenergic negative feedback voltage amplifier. The controller of the amplifier is modeled as a nullor with equivalent input noise sources \(V_{n}\) and \(I_{n}.\) Transformation of the noise sources from the input port of the nullor to the input port of the voltage amplifier shows that the equivalent input noise sources of the feedback amplifier equal those of the nullor. Hence, the feedback network does not affect the amplifier’s noise performance.

Fig. 226 Noise behavior of a nonenergic negative feedback voltage amplifier.

This transformation proceeds as follows:

1. The voltage source \(V_{n}\) in series with the input of the nullor is already at the input of the amplifier (see Fig. 226A).

2. The current source \(I_{n}\) in parallel with the input of the nullor can be redirected over the ground terminal of the amplifier. This is shown in Fig. 226B. We then obtain a noise current source in parallel with the input of the amplifier and a correlated current source in parallel with the transformer.

3. The source in parallel with the transformer can be replaced with a current source \(I_{n}/n_{1}\) in parallel with the other port of the transformer, as shown in Fig. 226C. This source can be ignored, because it is in parallel with the norator. Replacing it with equivalent input noise sources of the nullor would yield zero values for those sources.

The remaining noise sources are a voltage source \(V_{n}\) in series with the input of the amplifier and a current source \(I_{n}\) in parallel with the input of the amplifier. Those two sources thus equal the original noise sources at the input of the nullor. Hence, the feedback network does not affect the noise performance of the amplifier.

Power efficiency of nonenergic feedback amplifiers

The nonenergic feedback element does not degrade the power efficiency of the amplifier. This can easily be seen for the voltage amplifier from Fig. 226: its feedback element does not carry any current because one of the ports of the transformer is placed in series with the nullator.