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# n-channel MOSFET common source amplifier

#### studentLab

Apr 21, 2014
11
Hello and good day for all, I need advice in finding Vout and ac voltage gain in n-channel MOSFET common source amplifier.

Here i get :

Since the source is grounded, the gate-to-source voltage is
VGS = (R2 / (R1 + R2)) x Vdd

VGS = (33k / (51k + 33k)) x 15

VGS = 5.893V

ID = k [ VGS – VGS(th) ]2

Since: VGS = 7.5V, VGS(th) = 5V, ID = 5mA

Therefore : ID = k [ VGS – VGS(th) ]2

k = ID / [ VGS – VGS(th) ]2

k = 5mA / [7.5V - 5V]2

k = 0.8mAV-2

The Drain Current ID at VGS = 5.89V is ID = 0.8mAV-2 [ 5.89V – 5V ]2

ID = 0.8mAV-2 [ 5.89V – 5V ]2

ID = 0.634mA

The Drain Voltage is VD = VDS = 15V – [0.634mA x 3.3k]

VD = VDS = 15V – [0.634mA x 3.3k]

VDs = 12.90V

The Drain to source resistor is rDS = VDS / ID

rDS = 12.90V / 0.634mA

rDS = 20.35k

Rin = R1||R2

Rin = 51k x 33k / 51k + 33k

Rin = 1683k / 84k

Rin = 20.04k

ro = VM / ID

ro = 50V / 0.634mA

ro = 78.9k

Vout = −gmVgs(ro || RD) ----------------------> It is VGS same with Vgs?

Vout = -6mS Vgs ( 78.9k x 3.3k / 78.9 + 3.3k )

Vout = -6mS Vgs ( 3.17k )

Vout = -19.02 Vgs

#### studentLab

Apr 21, 2014
11
Vgs = ( Rin / Rin + 0 ) x Vin

Vgs = ( 20.04k / 20.04k + 0 ) x 45mV

Vgs = 45mV

Vin = Vgs

Vin = 45mV

Vout = −gmVgs(ro || RD)

Vout = -6mS x 45mV ( 78.9k x 3.3k / 78.9 + 3.3k )

Vout = -6mS x 45mV ( 3.17k )

Vout = -0.856V

Ac output gain = Av = Vout / Vin

Av = -0.856V / 45mV

Av = -19.02

Do i doing right here?

#### Ratch

Mar 10, 2013
1,098
Hello and good day for all, I need advice in finding Vout and ac voltage gain in n-channel MOSFET common source amplifier.

Here i get :

Since the source is grounded, the gate-to-source voltage is
VGS = (R2 / (R1 + R2)) x Vdd

VGS = (33k / (51k + 33k)) x 15

VGS = 5.893V

ID = k [ VGS – VGS(th) ]2

Since: VGS = 7.5V, VGS(th) = 5V, ID = 5mA

Therefore : ID = k [ VGS – VGS(th) ]2

k = ID / [ VGS – VGS(th) ]2

k = 5mA / [7.5V - 5V]2

k = 0.8mAV-2

The Drain Current ID at VGS = 5.89V is ID = 0.8mAV-2 [ 5.89V – 5V ]2

ID = 0.8mAV-2 [ 5.89V – 5V ]2

ID = 0.634mA

The Drain Voltage is VD = VDS = 15V – [0.634mA x 3.3k]

VD = VDS = 15V – [0.634mA x 3.3k]

VDs = 12.90V

The Drain to source resistor is rDS = VDS / ID

rDS = 12.90V / 0.634mA

rDS = 20.35k

Rin = R1||R2

Rin = 51k x 33k / 51k + 33k

Rin = 1683k / 84k

Rin = 20.04k

ro = VM / ID

ro = 50V / 0.634mA

ro = 78.9k

Vout = −gmVgs(ro || RD) ----------------------> It is VGS same with Vgs?

Vout = -6mS Vgs ( 78.9k x 3.3k / 78.9 + 3.3k )

Vout = -6mS Vgs ( 3.17k )
Vout = -19.02 Vgs

For calculating K you are using a formula for the triode region of the MOSFET. Besides, you left out the Vds term. I think you want to use the formula for the saturated region which is Id = K*(Vgs-Vt)^2 , which gives K=0.006272 .

Ratch

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