33.5.3. Voltage Gain

The expression of the voltage gain A is defined as v_out / v_in = -R_D × g_m.

Voltage gain is a measure of the amplification provided by the amplifier. In this expression, v_out is the output voltage, and v_in is the input voltage. The term -R_D × g_m indicates that the output voltage is influenced by the drain resistance (R_D) and the transconductance (g_m) of the MOS transistor. The negative sign implies that the output is inverted relative to the input.

Think of the voltage gain like a loudspeaker amplifying sound. If you speak into a microphone (input voltage), the loudspeaker produces a louder sound (output voltage), but sometimes the loudness can also change the pitch, similar to the inversion seen in voltage gain.

The second parameter is the output resistance. It can be represented as R = v_x / i_x, where we observe the output current.

Output resistance is important because it affects how the amplifier interacts with the load connected to it. To calculate it, we substitute v_x as the voltage across the load and i_x as the output current flowing through that load. This helps in designing for how the amplifier will behave with actual devices it may connect to.

Consider output resistance like the flow of water in a pipe. The resistance the water encounters affects how forcefully it comes out of the other end. If the output resistance is high, it may limit how much water (or current) can flow through, affecting the performance of the system.

The input resistance can be calculated assuming the gate current is 0. The input resistance can be expressed as R = R1 || R2.

Input resistance refers to how much resistance the signal source feels when it connects to the amplifier's input. In this case, R1 and R2 are resistors connected in parallel, which decreases the total resistance seen by the input signal. This is crucial for ensuring minimal loss of input signal strength.

Imagine plugging your phone charger into an outlet. The outlet provides the electrical resistance that your charger sees. If there are two outlets next to each other, and you can plug into either, it’s akin to connecting resistors in parallel. You get better access to power by using both instead of just one.

When the circuit is mapped into a voltage amplifier, we observe A, R_v, and R_o at the output.

Mapping the circuit into a voltage amplifier means we are representing it as a simple model where we can easily analyze voltage gain and resistances. A is the voltage gain, R_v is the input resistance seen from the source, and R_o is the output resistance. This simplification aids in the design process.

Think of mapping the circuit like creating a simplified map of a city. Instead of showing every street and building, you focus on the major highways and landmarks so that someone can easily navigate to their destination.

If the output is a current, the amplifier functions as a transconductance amplifier where G = -A_v / R_o.

In this scenario, the amplifier is set up such that it outputs a current instead of a voltage. The relationship G = -A_v / R_o defines the transconductance, illustrating how much output current is gained per input voltage signal compared to the output resistance.

This can be thought of as how a pump moves water through different outlets. Depending on how much pressure you apply (input voltage), the pump can push out a specific amount of water (output current). The design of the pump (output resistance) affects how effectively water is delivered.

In high frequency situations, parasitic capacitances such as gate-to-source capacitance must be considered.

At high frequencies, additional effects such as parasitic capacitances (which are unintended capacitances between components) can influence behavior, causing issues like signal attenuation. Recognizing these is essential in designing circuits that operate effectively at high frequencies.

This is similar to fast cars encountering wind resistance as they speed up. The faster they go, the more drag they feel. In circuits, these parasitic capacitances introduce new resistive 'drag' at higher frequencies that can degrade performance.

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