Equations

Below are some of the main equations that I have found useful to have on hand.

Use ./generateTables.sh ../src/es2c0/equations.md  in the scripts folder.

Oscillators

Closed Loop Gain

• is the closed loop gain of the system.
• is the open loop gain (with no feedback)
• is the feedback fraction, that feeds back a portion of the output voltage back to the input

Loop Gain

For oscillation, need unity gain, so angle therefore must be real, so also must be real.

Transfer function of CR Network

= Gain of CR network

Transfer function of RC Network

= Gain of RC network

AC BJT Analysis

Transistor Input Impedance

Where = 25mV, = Collector current at Q point.

Input Impedance of Collector Follower (Common Emitter)

Into the transistor

Output Impedance of Collector Follower (Common Emitter)

As current source has infinite impedance.

Emitter Follower (Common Collector)

• High Input, low ouput impedence
• High current gain
• So acts as impedence trasnformer and buffer

Voltage Gain of Emitter Follower (Common Collector)

as So low voltage gain, so instead current amplifier.

Output Impedence of Emitter Follower (Common Collector)

Where = source input impedance

Output Impedence of Emitter Follower (Common Collector) Simple

Where = source input impedance

MOSFETs DC

No current through gate in MOSFET (as voltage controlled) (infinite input impedence)

Stages

• Cut off (no current flows,
• Linear
• Saturation

Where = Threshold Voltage

Linear Region Drain Current

, where = transconductance constant

MOSFET Bias Network

Must check the two different values to see which ones are valid solutions.

MOSFET input impedence

As no current flows into gate

MOSFET Common Source

Similar to BJT common emmitter amplifier

Overall Input Impedence

As two gate bias resistors act as impedances to input signals. Therefore used over BJTs when high impedence required.

Is actually in parallel with source (input) impedence if it has it.

Overall Output Impedance

As current source has infinite impedence, therefore is the only impedence seen.

Unless there is an which would be in parallel with .

Differential Amplifier

Long tail pair:

Modes Can operate in two modes.

• Differential (Amplfies Difference between two input signals)
• Common mode (Works similar to regular BJT amp)

Common Mode Same signal is connected to both input terminals.

• Ideal differential amp rejects common mode input, but not realistic
• Defined by CMRR

Better amps, have high ratio of differnetial to common gain, AKA Common Mode Rejection Ratio (CMRR).

Quiescent Current of Long Tail Pair

Current through shared emitter resistor, .

Biasing

and are grounded, therefore collector voltages are the same.

Collector Voltage of Grounded Long Tail Pair

And for matched transistors, .

Not really used

Generalised Differential Amplifier Output

Both common mode and differential mode input signals are factored in.

Op-Amps

Active Filter Gain, Z2 = R2 || C

• Low Pass filter
• Cutoff where = Hz

Misc

Source Regulation

Fraction of change in load and input voltage