Linear Circuits and RC Circuits

A circuit where output is directly proportional to input, and superposition applies.

The total response to multiple inputs is the sum of responses to individual inputs.

The output is directly proportional to the input.

Circuit characteristics do not change with time.

A circuit using resistors and capacitors.

Resistors, capacitors, inductors, op-amps, and transistors.

Well-defined characteristic of a linear circuit, calculated from resistance, reactance and other components.

Linear circuits can be designed to operate within stable limits using feedback mechanisms(e.g. in op-amps).

An ideal op-amp has infinite input impedance, zero output impedance, and infinite open-loop gain. These characteristics ensure perfect amplification and isolation.

The gain of the op-amp without any feedback, typically very high (10^5 to 10^6).

The range of frequencies over which the op-amp can maintain its specified gain.

The maximum rate of change in the output voltage, usually measured in V/µs.

A simple circuit that divides an input voltage into smaller, proportional parts using two resistors.

The output voltage of a voltage divider is calculated by multiplying the input voltage with the ratio of the second resistor to the total resistance.

A transistor amplifier circuit where the input signal is applied to the base, the output is taken from the collector, and the emitter is grounded.

Common-emitter amplifiers are widely used in audio and RF applications due to their ability to amplify voltage.

The behavior of an RC circuit is determined by the interaction between the resistor, which opposes current flow, and the capacitor, which stores energy in an electric field. This interaction leads to frequency-dependent characteristics.

Impedance in an RC circuit is the total opposition to current flow. It is represented as ZRC = R + 1/jωC, where R is resistance, C is capacitance, and ω is angular frequency.

The cutoff frequency (fc) in an RC circuit is the frequency at which the impedance of the resistor and capacitor are equal. This is the point where the circuit transitions between passing and blocking frequencies.

The time constant (τ) in an RC circuit is the time it takes for the voltage across the capacitor to rise to 63% of its final value during charging or decay to 37% during discharging. It's calculated as τ = RC.

RL circuits are mainly used for filtering and in applications where inductance plays a critical role, such as power supplies and radio-frequency circuits.

Impedance in an RL circuit is the total opposition to current flow. It's defined as ZRL = R + jωL, where R is resistance, L is inductance, and ω is angular frequency.

The cutoff frequency (fc) in an RL circuit separates frequencies passed and blocked. It's determined by fc = R/(2πL), where R is resistance and L is inductance.

The time constant (τ) in an RL circuit represents the time it takes for the current through the inductor to reach approximately 63% of its final value. It's given by τ = L/R.