Transfer Function

Derivation of the Transfer Functions for Error Amplifiers, Voltage Amplifiers, Current Amplifiers

2016.11.24

Points of this article

・It is confirmed that general transfer functions for a voltage amplifier and a current amplifier can be derived from the derived transfer function for an error amplifier.

table of contents

・Transfer function of an error amplifier
・Transfer function of a voltage amplifier
・Transfer function of a current amplifier

Fig. 1

Transfer function of an error amplifier

Figure1 is an example of a general error amplifier block. This amplifier compares V_in and V_ref, and outputs the results as V_c. Here we derive the transfer function for this amplifier, but first, confirm for yourself that Z₁, Z_b and Z_t are as follows for the circuit blocks surrounded by dashed lines in the diagram.

Next, Kirchhoff’s laws are used to derive the transfer function (Δv_c/Δv_in) for the amplifier of Fig. 1.

The Kirchhoff laws used in the derivation are shown in eq. 2-1.

Next, the transfer function derived using eq. 2-1 is shown in eq. 2-2.

Eq. 2-2 can be treated as a general equation for the transfer function of an error amplifier such as that of Fig. 1. Below, eq. 2-2 is used to examine the transfer functions of “a voltage amplifier” and “a current amplifier”, which are essential when considering DC-DC converters.

Fig. 2

Transfer function of a voltage amplifier

Fig. 2 shows an example of a voltage amplifier configuration. Eq. 2-3 below is a general relationship, appearing on data sheets and the like, for the transfer function of a voltage amplifier.

We check whether we can derive this eq. 2-3 using the previously derived eq. 2-2. The conditions for eq. 2-2 are as follows.

Modifying eq. 2-2 based on these conditions, we arrive at eq. 2-4.

Here, when eq. 2-4 satisfies the conditions of eq. 2-5 below, eq. 2-4 can be expressed as eq. 2-6:

Compare this eq. 2-6 with eq. 2-3 above, presented as a general equation for the transfer function of a voltage amplifier. You should be able to see that the two are equivalent.

Fig. 3

Transfer function of a current amplifier

Next, Fig. 3 shows an example of a current amplifier configuration. Eq. 2-7 below is likewise the equation generally used for the transfer function of this amplifier.

Now we similarly attempt to derive eq. 2-7 using eq. 2-2. The conditions for eq. 2-2 are as follows.

Modifying eq. 2-2 based on this, we can derive the following eq. 2-8.

Upon comparison with eq. 2-7, it should again be clear that the two are equivalent.

Thus it is seen that transfer functions for a voltage amplifier and a current amplifier can be derived from the transfer function for the error amplifier of Fig. 1 derived in the beginning.

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