Revision as of 15:37, 8 January 2010

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 take two (or more) input sources that produce an output voltage proportional to the difference between the input voltages. $V_{o}=A_{d}(v_{i1}-v_{i2})\,$ , where $A_{d}\,$ is the differential gain
Instead of expressing the input voltages in terms of $v_{i1}\,$ $v_{i1}\,$ and $v_{i2}\,$ $v_{i2}\,$ , we can express it in terms of the differential and common-mode input.
- 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

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

@@ Line 53: / Line 53: @@
 **Common-mode input signal is the average of the input voltages. <math>v_{icm}=\frac{1}{2}(v_{i1}+v_{i2})</math>
 **<math>v_{i1}=v_{icm}+\frac{v_{id}}{2}</math>, if <math>v_{i1}\,</math> is the positive terminal
-****<math>v_{i2}=v_{icm}-\frac{v_{id}}{2}</math>, if <math>v_{i2}\,</math> is the negative terminal
+**<math>v_{i2}=v_{icm}-\frac{v_{id}}{2}</math>, if <math>v_{i2}\,</math> is the negative terminal
 **See Figure 1.44 on page 49 for a good visual reference