48.1.8. Voltage Gain for Common Drain Amplifier

The voltage gain A is defined by the expression $A_v = \frac{g_m \cdot r_o}{r_o + R_E}$, where $R_E$ is the emitter resistance. This formula shows that the gain is influenced by the transconductance ($g_m$) and the output resistance ($r_o$).

The voltage gain of a common drain amplifier indicates how much the output voltage changes in response to a change in input voltage. The formula involves transconductance, which represents the amplifier's ability to convert input voltage to output current. The output resistance is also crucial because it affects how much of the input gets passed through to the output. As $R_E$ increases, the gain decreases because more voltage is dropped across the emitter resistor, reducing the output.

Think of the amplifier as a water faucet. The input voltage is like the water pressure in the pipes. If the faucet is wide open (low $R_E$), a small increase in water pressure will produce a large increase in the flow of water (output voltage). If you partially close the faucet (high $R_E$), the flow will not change as dramatically because much of the pressure is 'used up' at the faucet.

The output impedance of the common drain amplifier, denoted as $R_{out}$, is close to the value of the load resistance when viewed from the output side of the device.

Output resistance affects how the amplifier behaves when connected to a load. If the load resistance is comparable to the output impedance, the voltage gain will decrease based on how much of the signal is dropped across this impedance. Ideally, you want a low output impedance compared to the load to maximize power transfer.

Imagine a delivery truck (the amplifier) trying to deliver goods (the output signal) to a store (the load). If the road (output resistance) is bumpy and the truck can't carry much (low output impedance), the amount of goods that actually reach the store is reduced. If the road is smooth (low resistance), more goods can be efficiently delivered.

Having a high emitter resistance can reduce the voltage gain further, leading to effective amplification that becomes closer to unity (around 1), meaning that the output signal becomes similar to the input signal.

When the emitter resistance is high, the amplifier is less effective at providing gain, essentially acting more like a buffer than an amplifier. This means that even though the device is still amplifying, the degree of amplification is minimal, resulting in more of a replication of the input than true amplification.

Consider using a megaphone (amplifier) to make your voice louder. If you put a thick blanket over the megaphone’s mouth (high emitter resistance), your voice will still come out, but it'll be muffled and quieter (lower gain) compared to if it were fully uncovered. Essentially, you'll hear your voice but not as clearly.

Despite changes in output resistance and emitter resistance, the overall performance of the common drain amplifier maintains a high input impedance and low output impedance, fulfilling its function as a buffer.

The common drain amplifier is designed to have high input impedance, which means it does not load down the previous stage (like a light load on a battery). This is crucial in maintaining the integrity of the signal coming from the previous stage. Meanwhile, a low output impedance allows for effective signal transfer to the next stage with minimal loss.

Think of a good relay race team. The first runner (previous stage) passes the baton (signal) to the next runner (common drain amplifier). If the first runner has a light grip (high input impedance), they won’t drop the baton. The next runner should also have a steady hand (low output impedance) to ensure a smooth handover without dropping it, ensuring the race (signal flow) continues seamlessly.

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