Solutions for Homework 6: Electronic Circuits Analysis, Exercises of Electronics

The solutions to problem set hw6 in the context of electronic circuits analysis. It includes calculations for transconductance (gm) and output resistance (rout) for various circuit configurations, as well as the determination of voltage gain (av) using these values. The document also presents the small signal model of the circuit and its analysis.

Typology: Exercises

2019/2020

Uploaded on 01/17/2020

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Solutions for HW6
Divija Gogineni
October 24, 2019
(7.33)
(a)
From Eg. (7.71)
Rout = (1 + gm1ro1)1
gm2+ro1
(b)
From Eg (7.71)
Rout = (1 + gm1ro1)1
gm2+ro1
(c)
From Eg (7.71)
Rout = (1 + gm2ro2)(ro1|| 1
gm3) + ro2
(d)
From Eg. (7.71)
Rout = (1 + gm1ro1)(ro2|| 1
gm3) + ro1
(7.42)
Voltage gain, Av=GmRout,
where Gmand Routare the transconductance and output resistance
of the circuit respectively.
To find Gm:
1
pf3

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Solutions for HW

Divija Gogineni

October 24, 2019

(a)

From Eg. (7.71)

Rout = (1 + gm 1 ro 1 ) gm^12 + ro 1

(b)

From Eg (7.71)

Rout = (1 + gm 1 ro 1 ) gm^12 + ro 1

(c)

From Eg (7.71)

Rout = (1 + gm 2 ro 2 )(ro 1 || gm^13 ) + ro 2

(d)

From Eg. (7.71)

Rout = (1 + gm 1 ro 1 )(ro 2 || gm^13 ) + ro 1

Voltage gain, Av = GmRout,

where Gmand Routare the transconductance and output resistance

of the circuit respectively.

To find Gm :

Gm = i Voutin = gm + r^1 o ≈ gm (Since gmro >> 1)

To find Rout:

Rout = RD ||R 1

=RD ||[(1 + gmro)RS + ro] From Eg. (7.110)

≈ RD ||(gmroRS + ro) (Since gmro >> 1)

= g RmDro +RgSm^ RrDoR^ +Sr +oRroD

Therefore, voltage gain=gm

[

gmroRD RS +roRD RD +gmroRS +ro

]

The small signal model is :

Since −io = i 1 + i 2 + i 3

−gm(vg − vin) = Rv 2 out+R 1 + v Rout 3 +−Rvin 4 + v RoutD

gm

vin − R 1 R+^1 R 2 vout

= vout

R 1 +R 2 +^

R 3 +R 4 +^

RD

− R 3 v+inR 4

vin

gm + R 3 +^1 R 4

= vout

gmR 1 +

R 1 +R 2 +^

R 3 +R 4 +^

RD

vout

vin =

gm+ (^) R 31 +R 4

R^1 D +^ R^1 3 +R 4 +^ gmR 1 + R 1 +R 2