Chapter 1

Amplifier Models

• These are purely models, and cannot be replicated in a real world environment. They are meant to explain.
• Trans stands for transfer (from voltage to current or visa versa)
• The inputs and outputs can be either current or voltage. This leads to 4 amplifier models.
• You can use any of these models, though some may be easier to work with (if you are given the Thevenin or Norton equivalent)

Amplifier models

Amplifier type Gain parameter Gain equation	Voltage input	Current input
Voltage output	Voltage Open-circuit voltage gain $A_{voc}={\frac {v_{ooc}}{v_{i}}}$	Transresistance Open-circuit transresistance gain $R_{moc}={\frac {v_{ooc}}{i_{i}}}$
Current output	Transconductance Short-circuit transconductance gain $G_{msc}={\frac {i_{osc}}{v_{i}}}$	Current Short-circuit current gain $A_{isc}={\frac {i_{osc}}{i_{i}}}$

Characteristics of ideal amplifiers

Amplifier Type	Input Impedance	Output Impedance	Gain Parameter
Voltage	$\infty$	0	$A_{voc}\,$
Current	0	$\infty$	$A_{isc}\,$
Transconductance	$\infty$	$\infty$	$G_{msc}\,$
Transresistance	0	0	$R_{moc}\,$

Differential Amplifiers

• Differential amplifiers take two (or more) input sources that produce an output voltage proportional to the difference between the input voltages.
• Instead of expressing the input voltages in terms of $v_{i1}\,$ and $v_{i2}\,$, we can express it in terms of the differential and common-mode input. Why?
  • Differential input signal is the difference between the input voltages. $v_{id}=v_{i1}-v_{i2}\,$
  • Common-mode input signal is the average of the input voltages. $v_{icm}={\frac {1}{2}}(v_{i1}+v_{i2})$
  • $v_{i1}=v_{icm}+{\frac {v_{id}}{2}}$, if $v_{i1}\,$ is the positive terminal
  • $v_{i2}=v_{icm}-{\frac {v_{id}}{2}}$, if $v_{i2}\,$ is the negative terminal
  • See Figure 1.44 on page 49 for a good visual reference
• $v_{o}=A_{d}v_{id}+A_{cm}v_{icm}\,$, where $A_{d}\,$ is the differential gain and $A_{cm}\,$ is the common mode gain
• The common-mode rejection ratio (CMRR) is the ratio of the magnitude of the differential gain to the magnitude of the common-mode gain
  • In decibels $CMRR=20\log {\frac {|A_{d}|}{|A_{c}m|}}$

Definitions

• Input Resistance: $R_{i}$ of an amplifier is the equivalent resistance seen when looking into the input terminals
• Output Resistance:$R_{o}$ is the Thevenin resistance seen when looking back into the output terminals of an amplifier
• Open-circuit voltage gain: the ratio of output amplitude to input amplitude with the output terminals open circuited
• Short-circuit current gain: the current gain with the output terminals of the amplifier short circuited

Bag of Tricks

• Buffer amplifier is used to transfer voltage but not current to the following circuit. This amplifier can be used to negate the loading effects. No current flows through the amplifier, thus there is no voltage drop through the input resistor (going to the buffer amplifier).

Buffer Amplifier

• Inverting amplifier uses negative feedback to invert and amplify voltage. Using nodal analysis at the negative terminal, the gain is found to be $-{\frac {R_{2}}{R_{1}}}$

Inverting Amplifier