93.1.7. Trans-Conductance Amplifier Configuration

So, here we do have the trans-conductance amplifier here and the forward amplifier it is you can see here the signal it is current and the signal here it is voltage. So, the mixing here it is series and sampling here it is also series. So, this is series connection or current sampling series mixing feedback network.

The trans-conductance amplifier is a type of amplifier that converts an input current into an output voltage. In this configuration, both the sampling and mixing are done in series, meaning the components are arranged in such a way that the output is affected directly by the input current. When we say 'forward amplifier', we refer to the part responsible for amplifying the signal, which in this case introduces a current input and voltage output relationship.

Imagine a water faucet (representing the current input) connected to a water tank (representing the output voltage). When you turn the faucet on (input current), water flows into the tank (output voltage) and fills it up, demonstrating how a small change in the current can significantly affect the amount of water in the tank.

Here also it will be very similar to our previous discussion as we said that to get the output resistance. So, we need to stimulate this circuit by one voltage source and then we can observe the corresponding current here. Keeping the input port condition it is supporting the feedback network namely we are keeping the source with a source signal of 0.

To determine the output resistance of a trans-conductance amplifier, we apply a voltage to the circuit and measure the resulting current. This method tests how much the output responds to changes in input conditions. Specifically, we maintain a condition where the input source has zero signal so that we can effectively isolate the feedback network’s behavior without external interference.

Think of a factory assembly line where you add a piece and measure how many products are produced as a result. If you shut off any raw material input (keeping the source signal at zero), you can see how the assembly line performs purely based on existing conditions and configurations without outside influence.

In ideal condition to start with we are considering source term in equivalence equivalent source resistance = 0. So, from that we can say v = ‒ v.

In an ideal scenario, we assume that there is no resistance affecting the input or output, which allows us to analyze the circuit's performance without the complications of real-world resistance values. This simplifies our calculations and helps us understand the theoretical maximum efficiency of the amplifier's operation.

Imagine trying to push a toy car on a perfectly smooth and frictionless surface (ideal condition). The car would move without any impediments. In practical scenarios with a rough surface (resistance), the car’s speed would reduce, just as real amplifiers' output would decrease due to resistive losses.

So, let me clear again clear the board and let we continue the discussion. Now, if we consider non-ideal factors namely if I consider this is nonzero, then I have to consider the corresponding β′.

When we introduce non-ideal conditions, such as finite resistances, these factors directly influence the operational performance of the amplifier. The parameter β' represents the adjusted feedback factor considering these resistances in the circuit, which directly impacts the output resistance we are measuring.

Think of a sprinter running on a track. Normally, the track is perfect (ideal conditions), allowing fast, unhindered performance. However, if the track has obstacles (non-ideal conditions), the sprinter’s speed is adversely affected, similar to how resistances affect an amplifier's performance.

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