320-amp-models.tex Page 1 ECE 320. Amplifier Models. ECE Linear Active Circuit Design

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1 320ampmodels.tex Page 1 ECE 320 Amplifier Models ECE 320 Linear Active Circuit Design

2 320ampmodels.tex Page 2 2Port Networks A 2port network is any circiut with two pairs of wires connecting to the outside world. (Each port is a pair of wires.) The standard notation used for the voltages and currents in a 2port network is shown below. i 1 i 2 v 1 2port network v 2 Just as there are two completely equivalent models for a 1port network (the Thévenin and Norton equivalent circuits), there are multiple equivalent models for a 2port network. We will consider the z, y, g, and h parameter models. (There are also s and abcd parameters.) ECE 320 Linear Active Circuit Design

3 320ampmodels.tex Page 3 z Parameters i 1 i 2 v 1 z 11 z 21 i z 1 22 z 12 i 2 v 2 v 1 = z 11 i 1 z 12 i 2 v 2 = z 21 i 1 z 22 i 2 ECE 320 Linear Active Circuit Design

4 320ampmodels.tex Page 4 z 11 = v 1 i 1 z 12 = v 1 i 2 z 21 = v 2 i 1 z 22 = v 2 i 2 = opencircuit input resistance i2 =0 = reverse opencircuit transresistance i1 =0 = forward opencircuit transresistance i2 =0 = opencircuit output resistance i1 =0 All of the z ij are in Ohms. ECE 320 Linear Active Circuit Design

5 320ampmodels.tex Page 5 y Parameters i 1 i 2 v 1 1 y 11 y 12 v 2 y 21 v 1 1 y22 v 2 i 1 = y 11 v 1 y 12 v 2 i 2 = y 21 v 1 y 22 v 2 ECE 320 Linear Active Circuit Design

6 320ampmodels.tex Page 6 y 11 = i 1 = shortcircuit input conductance v2 =0 v 1 y 12 = i 1 = reverse shortcircuit transconductance v1 =0 v 2 y 21 = i 2 = forward shortcircuit transconductance v2 =0 v 1 y 22 = i 2 = opencircuit output conductance v1 =0 v 2 All of the y ij are in Siemens. ECE 320 Linear Active Circuit Design

7 320ampmodels.tex Page 7 g Parameters i 2 v 1 1 g 11 g 21 v g 22 1 g 12 i 2 v 2 i 1 = g 11 v 1 g 12 i 2 v 2 = g 21 v 1 g 22 i 2 ECE 320 Linear Active Circuit Design

8 320ampmodels.tex Page 8 g 11 = i 1 = opencircuit input conductance i2 =0 v 1 g 12 = i 1 = reverse shortcircuit current gain v1 =0 i 2 g 21 = v 2 = forward opencircuit voltage gain i2 =0 v 1 g 22 = v 2 i 2 = shortcircuit output resistance v1 =0 g 12 and g 21 are dimensionless, while g 11 is in Siemens and g 22 is in Ohms. ECE 320 Linear Active Circuit Design

9 320ampmodels.tex Page 9 h Parameters i 1 i 2 v 1 h 11 h 12 v 2 h 21 i 1 1 h22 v 2 v 1 = h 11 i 1 h 12 v 2 i 2 = h 21 i 1 h 22 v 2 ECE 320 Linear Active Circuit Design

10 320ampmodels.tex Page 10 h 11 = v 1 i 1 h 12 = v 1 v 2 h 21 = i 2 i 1 h 22 = i 2 v 2 = shortcircuit input resistance v2 =0 = reverse opencircuit voltage gain i1 =0 = forward shortcircuit current gain v2 =0 = opencircuit output conductance i1 =0 h 12 and h 21 are dimensionless, while h 11 is in Ohms and h 22 is in Siemens. ECE 320 Linear Active Circuit Design

11 320ampmodels.tex Page 11 IEEE Alternative Subscript Notation 11 i for input 12 r for reverse transfer 21 f for forward transfer 22 o for output ECE 320 Linear Active Circuit Design

12 320ampmodels.tex Page 12 Amplifiers An amplifier is a special case of a 2port network having an input port and an output port. Amplifiers are considered to be onedirectional, producing a scaled copy of the input signal at the output port. Standard amplifier models are used in system design in much the same way as the Thèvenin and Norton models: they provide the simplest possible description of the properties of a more complex circuit. Thus, the parameters of the standard amplifier models are used in specifications. ECE 320 Linear Active Circuit Design

13 320ampmodels.tex Page 13 The circuit below shows an amplifier, together with a model for the source that drives it, and the load. The definitions of a number of commonlyused parameters are also given. R L i i v S v o R L Input voltage gain: A v = v o vi Overall voltage gain: A vs = v o v S Current gain: A i = ii Transresistance: R m = v o ii Input transconductance: G m = vi Input power gain: A p = p o p i = v o vi ii = A v A i Overall power gain: A ps = p o p s = v o v s ii = A vs A i ECE 320 Linear Active Circuit Design

14 320ampmodels.tex Page 14 Amplifier Models There are four equivalent amplifier models. Each one can be derived from one of the 2port network parameterizations by setting the parameter with the subscript 21 to zero, renaming v 1. v 2 and i 1 to, v o and i i, changing the direction of i 2 and naming the new current. Thus there are four amplifier models, which are discussed in detail on the next few slides. ECE 320 Linear Active Circuit Design

15 320ampmodels.tex Page 15 Voltage Amplifier R S R o v S R i A vo v o R L A vo = v o io =0 = open circuit voltage gain The voltage amp comes from the gparameter 2port model. The figure below shows how. i 2 v 1 R i A vo 1 g 21 v g 22 1 g 11 g 12 i 2 0 R o v 2 v o ECE 320 Linear Active Circuit Design

16 320ampmodels.tex Page 16 R S R o v S R i A vo v o R L The voltage amplifier, together with its source and load, are used to connect the specific amplifier model with quantities describing the amplifier s performance. A v = v o = ( RL A vs = v o v S = v o v S = A i = i i = v o/r o /R i = R i R o v o = ) A vo = input voltage gain R o R L ( ) Ri A v = overall voltage gain R S R i ( ) Ri A v = current gain R o ECE 320 Linear Active Circuit Design

17 320ampmodels.tex Page 17 Current Amplifier R S v S i i R i R o A isi i v o R L A is = i i vo =0 = short circuit current gain A i = i i = ( Ro ) A is = input current gain R o R L ECE 320 Linear Active Circuit Design

18 320ampmodels.tex Page 18 Transconductance Amplifier R S v S R i R o G ms v o R L G ms = vo =0 = short circuit transconductance G m = = ( Ro ) G ms = input transconductance R o R L ECE 320 Linear Active Circuit Design

19 320ampmodels.tex Page 19 Transresistance Amplifier R S R o v S i i R i R mo i i v o R L R mo = v o i i Io =0 = open circuit transconductance R m = v o i i = ( RL ) R mo = input transconductance R L R o ECE 320 Linear Active Circuit Design

20 320ampmodels.tex Page 20 Conversion Between Amplifier Models Let s find the component values of a voltage amp that is equivalent to a given current amp. R S R S R o v S i i R i R o A isi i v o R L v S R i A vo v o R L Current Amp Voltage Amp Neither R o or R i needs a new value, although R o changes from parallel to seriesconnected. A vo = v o io =0 = R oa is i i = R oa is /i i = R o R i A is Note that this final expression contains only component values, and that all the voltages and currents have been eliminated. ECE 320 Linear Active Circuit Design

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