An amplifier has an input resistance of 1 Ωan output resistance of 1 Ω, and an open circuit volt

step 1 In this problem we have ri is equal to 1 om r not is equal to 1 om A voc is equal to 10 R s is e

An amplifier has an input resistance of 1 Ωan output...

An amplifier has an input resistance of $1 \Omega$ an output resistance of $1 \Omega,$ and an open circuit voltage gain of 10 . Classify this amplifier as an approximate ideal type and find the corresponding gain parameter. In deciding on an amplifier classification, assume that the source and load impedance are on the order of $1 \mathrm{k} \Omega.$

Key Concepts

Ideal Amplifier Models

There are several ideal amplifier types – for example, an ideal voltage amplifier has infinite input resistance and zero output resistance, while an ideal current amplifier has zero (or very low) input resistance and infinite output resistance. In some cases, it is more useful to think in terms of a transconductance or a transresistance amplifier. In a transresistance amplifier the input is a current (usually because the input resistance is very low) and the output is a voltage; its gain is expressed in ohms. Choosing which idealization to use depends on how the actual input and output impedances compare with the source and load values.

Input/Output Impedance and Loading Effects

The actual input and output impedances of an amplifier determine how it interacts with real-world sources and loads. Here, with both the amplifier’s input and output resistances (1 ?) being much smaller than the typical external impedances (1 k?), the loading effects are severe. That is, almost all of the source voltage is dropped across the source impedance (rather than the amplifier’s input) and the amplifier’s low output resistance causes only a small drop when driving the 1 k? load. Thus, the observed behavior of voltage amplification is really a consequence of the interaction between the amplifier’s internal resistances and the external circuit, making it more appropriate to analyze it as a current- (or, equivalently, a transresistance-) amplifier.

Transresistance Gain

A transresistance amplifier is characterized not by a voltage?gain, but by a gain parameter in ohms – the ratio of the output voltage to the input current. For the given amplifier, even though its nominal open?circuit voltage gain is 10, once the loading due to the 1 k? source and load is taken into account, the effective gain from the source current to the output voltage comes out to be roughly 10 ?. This is because nearly all of the voltage is dropped across the 1 k? impedances and only a small voltage (with respect to the source) appears across the 1 ? input resistance, making the overall behavior that of a transresistance amplifier.

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