Reduction of quantum fluctuation and suppression of the Gordon-Haus effect with phase-sensitive linear amplifiers

In small-signal analysis, a MOSFET transistor amplifier acts as a linear amplifier when operating in its saturation region. The gate-to-source voltage (VGS) of the MOSFET is the sum of the DC biasing voltage and the small time-varying input signal. This combination sets up the operating point and modulates the drain current (ID) that flows from the drain to the source. When a small AC signal is superimposed on the DC bias voltage at the gate, the instantaneous drain current comprises three...

The MOSFET, when operating in its active region, functions as a voltage-controlled current source. In this region, the gate-to-source voltage controls the drain current. This principle underlies the operation of the transconductance MOSFET amplifier. The output current is directed through a load resistor to convert this amplifier into a voltage amplifier. The output voltage is then obtained by subtracting the voltage drop across the load resistance from the supply voltage. This process results...

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.

Operational amplifiers (op-amps) are versatile electronic components that can be interconnected in a cascade - one after another in a linear sequence. This cascading is possible due to their infinite input resistance and zero output resistance, allowing them to maintain their input-output relationships even when connected in series.
In a cascaded system, each op-amp is referred to as a stage. The output of one stage drives the input of the subsequent stage. As the input signal passes through...