N-MOSFET Amplifier Common Source

 itutorial -  N channel MOSFET or often referred to as NMOS when using enhancement mode has the characteristic of normally off or does not conduct when there is no voltage at the  Gate-Source (V GS ) terminal , so the NMOS will conduct only if there is a positive voltage at the Gate-Source where the voltage is V GS must be greater than the threshold voltage  ( VTH ).  V TH  is the minimum voltage at the  Gate-Source terminal so that the MOSFET can flow electric current to the  Drain-Source terminal .

Characteristics of N-channel MOSFET enhancement mode

The characteristics of the NMOS enhancement mode shown in Figure 1 depict the transconductance slope plot when the voltage V DS remains constant or does not change with V GS changing from 0 to positive.

Figure 1. Characteristics of N-MOSFET enhancement mode

When the value of V GS is below the threshold voltage ( V TH ) then the N-MOSFET is in an off state or does not conduct electric current at the  Drain Source terminal even though there is voltage at the  Drain-Source terminal .

The amount of Drain current (I D ) in the N-MOSFET enhancement can be calculated using the formula: 

Where :

I D Q  : The amount of dc electric current flowing at the  Drain terminal .

k : The magnitude of the conductance parameter.
V GS Q  : The amount of dc voltage at the Gate-Source .
V TH  : The magnitude of the threshold voltage at the Gate-Source . 
V DS : Voltage at the Drain-Source terminal .

λ : Channel-length modulation  parameter

W: Gate width (Gate width)

The value of λ is very small in the order of zero point zero (0.00...) so that in calculations it can also be assumed that  λ is equal to zero , so that the magnitude of the current at the Drain terminal can be written as:

DC Bias N-Channel E-MOSFET

DC bias is used to determine the working point (Q point) . Q point is all functions of V GS , voltage source V DD , and load resistance at the  Drain terminal R D.

Figure 2. E-MOSFET working point

Figure 2 shows that in general the purpose of the dc MOSFET bias is so that the ac signal entering the MOSFET can be strengthened so that the peak of the output  signal is not cut off.

The bias voltage is generally set to a certain value so that the voltage at the  Drain-Source terminal  is half V DD so that the output signal can swing as much as possible without any signal being cut off.

Basic Common Source Amplifier Using N-Channel E-MOSFET

Figure 3 shows the basic amplifier circuit using a Common Source E-MOSFET with the following explanation:  

1. C 1 : Used to block dc current from flowing to the signal source. Apart from that, C 1 also functions as a coupling where the ac current will be superimposed on the dc current from the V DD source . C 1 also functions as a high pass filter  which will pass signals with a certain minimum frequency. 
2. C 2 : Used to block dc current from V DD  so that only ac current comes out of the capacitor. C 2 together with R D and R Load forms a high pass filter which transmits signals with a certain minimum frequency.
3. R 1 and R 2 are resistors to provide voltage to the  Gate terminal  so that the E-MOSFET can work. The magnitude of the voltage at the  Gate terminal  depends on the value of R 1 and R 2   with V G = [R 2 / (R 1  + R 2 )]. V DD 
4. Resistor R D is used to limit the current flowing at the  Drain and load terminals ( R Load )
5. R S : Used to get the voltage at the  Source terminal so that the desired V G S is obtained .

To explain further, the  Common Source MOSFET amplifier is given several component specification values ​​and some component values ​​need to be found yourself using calculations.

The following is the circuit specification data in Figure 3:

• VDD= 12 Volts, 
• VTH = 2 Volts
• k = 0.0006 A/V2
• RD= 3.3kΩ
• R
• λ = 0.01/Volt
• Ignoring Gate width (W) and Gate length(L) . 

The magnitude of the bias voltage V G is made 1/3 V DD .

Figure 3. Basic  N-MOSFET  amplifier mode enhancement

DC Analysis

DC analysis is used to determine the working point ( Q ) of a MOSFET using dc bias. When using dc analysis, all components at the capacitor terminal that are not connected to the dc source are removed because the capacitor functions to block dc current, so that the equivalent image of dc analysis in Figure 3 becomes as shown in Figure 4. 

Figure 4. DC analysis of N-MOSFET

Calculate all required component values ​​in Figure 4 with the data provided above:

Answer:

First step : Determine the value of I D Q.

To find the I D Q value , you must determine the voltage at the  Drain terminal . So that the wave can swing to the maximum, the voltage at the  output or Drain terminal is made 1/2 V DD so that:

V D = 0.5 . 12 Volts 

V D = 6 Volts.
I D Q = V D / R D
I D Q  = 6 Volts / 3300Ω

I D Q  = 1.82 mA

Second step: Find the voltage V GS that causes the N-MOSFET to conduct. In dc analysis the value of  λ can be ignored because the value is very small.

I D Q = k(V GS Q- V TH )2

V GS = √(I D /k) + V TH

V GS Q = √(0.00182 /0.0006) + 2
V GS Q  = 3.741 Volts

Third step : Find the Gate voltage ( VG ) and Source voltage VS :

V G = 1/3. V DD

V G = 1/3. 12 Volts

VG = 4 Volts

V GS Q  = V G -V S

V S = V G – V G S Q

V S = 4 Volts – 3.741 Volts

VS = 0.259 Volts

Fourth step : Find the V DS value

V DD = V D + V DS + V S

V DS = V DD – V D – V S

V DS = 12 – 6 – 0.259 Volts

V DS = 5.74 Volts

Fifth step : Find the resistance value of the resistor R S

R S = V S / I D Q

R S = 0.259 / 0.00182

R S = 142.3Ω

Sixth step : Find the values ​​of R 1 and R 2

V G = [R 2 /(R 1 + R 2 )]. V DD

V G = 1/3.V DD 

R 2 / (R 1 + R 2 ) = 1/3

Here determine the value of the resistor R 1 so that you can find the value of R 2 . So, if you take any resistor value commonly found on the market, for example R 1 = 200kΩ , then R 2 can be found:

R 2 / (200kΩ + R 2 ) = 1/3

3R 2 = 200kΩ + R 2

2R 2 = 200kΩ

R 2 = 100kΩ

The component values ​​resulting from dc analysis calculations are shown in Figure 5.

Figure 5. Components of dc analysis calculations

The working point ( Q ) of dc bias is shown in Figure 6.

Figure 6. Working point (Q) graph of dc N-MOSFET

Determine the values ​​of C 1 and C 2

To complete all the components of the amplifier circuit, including C 1 and C 2 , a frequency value is needed that will be passed into the amplifier circuit. For example, the amplifier  in Figure 3 is used to amplify sound signals, so the minimum frequency that can pass through the amplifier circuit  is 20Hz. To find the capacitor value in the MOSFET amplifier circuit, it can be done outside of ac analysis because the Gate terminal is considered not connected to any terminal so that the resistance at the Drain and Source terminals is not connected to the resistance or resistor at the Gate terminal .

Seventh step : Determine the value of C1 .

Capacitor C 1 together with R 1 and R 2 in Figure 3 are components of the high pass filter circuit which can be found using the formula:

C 1 = 1 / (2 . π . f . R in )

The value of R in can be found by parallelizing R 1 and R 2 :

1/R in = 1 / R 1 + 1 / R 2

R in = (R 1  . R 2 ) / (R 1 +R 2 )

R in = 200k.100k / (200k+100k)

R in = 66.67kΩ = 67kΩ

Then determine the minimum frequency that will be passed by the High Pass Filter . If the frequency is used to amplify a sound frequency signal then the minimum frequency passed is at least 20Hz so the value of C1 is :

C 1 = 1/(2 . π . f . R in )

C 1 = 1/(2 . π . 20 . 67kΩ)

C 1 = 0.119 µ F = 119 nF

Eighth step: Determine the value of C 2 .

C 2 = 1/(2 . π . f . R out )

The R out value can be found by parallelizing the R D and R out values .

1/ R ou t = 1/R D + 1/R Load

R out = R D . R Load / (R D + R Load )

R out = 3.3kΩ . 470 / (3.3kΩ + 470Ω)

R out = 411 Ω

So the value of C is 2

C 2 = 1/(2 . π . 20 . 411)

C 2 = 19.4µF 

From all the component values ​​calculated above, a picture of the amplifier circuit is shown in Figure 7. 

Figure 7. Common source N-MOSFET amplifier circuit

AC analysis

To determine the gain  it is necessary to use ac analysis and it should be noted that this analysis is intended for small signals . If the  input signal is large (large signal) , the N-MOSFET works in the saturation area where the drain current  is not linear to the input signal voltage so that distortion will occur in the output signal . Some transconductance equations that are commonly used in small signal  N-MOSFETs:

Where:
g m : Transconductance.
V GS  : Voltage at Gate Source  ac analysis.

V TH : Threshold voltage .
I D : Current at the ac analysis Drain terminal .

k n : Transconductance parameter

W:  Gate width (Gate width) 

L : Gate length (Gate length) 

In ac analysis, each capacitor will be considered short connected between its terminals. For the amplifier circuit in Figure 3, it is necessary to create an equivalent ac analysis circuit shown in Figure 8.

Figure 8.  Common source analysis equivalent circuit

From the AC analysis equivalent circuit image above, it is used to calculate the amount of MOSFET gain  .

The magnitude of the output voltage is:

The internal resistance value ( r o ) of the MOSFET can be found using the equation:

The value of V in can be found using the equation:

The amount of reinforcement or  gain of the amplifier circuit  is:

The value of  λ has a value  ranging between 0.1 to 0.001/Volt , so to simplify calculations  λ can be considered 0 ( λ.=0 ) .

So that :

r o = 1 / 0 = ∞ (very large), so r o can be ignored or does not exist. So r o in Figure 7 is considered non-existent and R S is excluded from the  output impedance because:

With r o =  ∞ then:

V out = g m .  V GS  . Z out

Z out  = R D  // R L oad

Z out  = 3300  Ω //10000 Ω

Z out  = 2481 Ω

g m = 2 . k. (V GS  – V TH )
g m  = 2 . 0.0006 . (3.741 Volts – 2 Volts)
g m = 0.0021 A/V
g m = 2.1 mA/V

A V   = (g m . Z o ut ) / (1 + g m .  R S )
A V   = (2.1mA/V  . 2481 Ω ) / (1 + 2.1mA/V  .  142 Ω )
A V   = (2.1mA/V  . 2481 Ω ) / (1 + 2.1mA/V  .  142 Ω )
A V  = (5.2) / (1.29)
A V = 4

Common Source Amplifier   uses a capacitor at the  Source terminal ( bypass capacitor ) .

The common source circuit  uses a bypass capacitor  , the same as the circuit in Figure 7, only there is a capacitor at the  Source terminal as shown in Figure 9. 

Figure 9.  Common source amplifier using  capacitor bypass

To determine the working point ( Q ) of the MOSFET is exactly the same as the dc analysis above. Meanwhile, for ac analysis to calculate the amount of gain for the amplifier circuit, it is shown in Figure 10.

Figure 10. Equivalent AC analysis circuit with a capacitor at the  source terminal

The ac analysis equivalent circuit of Figure 10 does not have R S even though it actually has R S in the  amplifier circuit. This is because in the AC equivalent circuit analysis each capacitor is considered short connected .  For small signals , r o is considered to be so large that it can be ignored.
From Figure 10 and r o is ignored, the magnitude of the gain of the  common source  amplifier circuit using a capacitor at the  source terminal is as follows:
V out  = g m  V GS . Z out
V in  = V GS -> K because capacitor C 3  is considered short-circuited.

So:
A V   =  V out /   V in 
A V   =  g m  V GS . Z out /   V GS
A V  =  g m  . Z out  

A V  = 2.1 mA/V . 2481 Ω
A V  = 5.2
From the ac analysis gain calculation it can be concluded that using a bypass in the common source can increase the signal gain.To determine the magnitude ofC 3 , it must be determined at what frequency the capacitor will work to help increase the gain. Because the amplifier circuit is intended to strengthen sound signals, when the frequency is 20Hz the capacitor can work to help increase the gain so thatC 3 can be found as follows: C 3 = 1 / (2 . π . f . R S ) C 3  = 1 / (2 . π . 20Hz . 142 Ω ) C 3  = 1 / (2 . π . 20Hz . 142 Ω ) C 3 = 56  µ F