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Unit – 6
Field Effect Transistor (FET) And MOSFET
CONSTRUCTION OF JFET
Figure 1: Symbol of n-channel FET Figure 2: Symbol of p-channel FET
PRINCIPLE OF JFET (n-Channel)
Drain characteristics of JFET
PRINCIPLE OF JFET (n-Channel)
Drain characteristics of JFET
When 𝑽𝑮𝑺 = 𝟎 and 𝑽𝑫𝑺 = 𝟎
When 𝑽𝑫𝑺 = 𝟎 and 𝑽𝑮𝑺 is decreased from zero
When 𝑽𝑮𝑺 = 𝟎 and 𝑽𝑫𝑺 is increased from zero
When 𝑽𝑮𝑺 is negative and 𝑽𝑫𝑺 is increased
CHARACTERISTICS PARAMETERS OF JFET
1. Mutual conductance or transconductance, 𝒈𝒎
𝑔𝑚 =
𝜕𝐼𝐷
𝜕𝑉𝐺𝑆 𝑉𝐷𝑆
=
Δ𝐼𝐷
Δ𝑉𝐺𝑆
, 𝑤𝑖𝑡ℎ 𝑉𝐷𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
2. Drain resistance, 𝒓𝒅
𝑟𝑑 =
𝜕𝑉𝐷𝑆
𝜕𝐼𝐷 𝑉𝐺𝑆
=
Δ𝑉𝐷𝑆
Δ𝐼𝐷
, 𝑤𝑖𝑡ℎ 𝑉𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
3. Drain conductance, 𝒈𝒅
𝑔𝑑 =
𝜕𝐼𝐷
𝜕𝑉𝐷𝑆 𝑉𝐺𝑆
=
Δ𝐼𝐷
Δ𝑉𝐷𝑆
, 𝑤𝑖𝑡ℎ 𝑉𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
4. Amplification factor, 𝝁
𝜇 = −
𝜕𝑉𝐷𝑆
𝜕𝑉𝐺𝑆 𝐼𝐷
= −
Δ𝑉𝐷𝑆
Δ𝑉𝐺𝑆
, 𝑤𝑖𝑡ℎ 𝐼𝐷 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Relationship among FET parameters or Relation between 𝝁, 𝒓𝒅 & 𝒈𝒎
𝐼𝐷 = 𝑓 𝑉𝐷𝑆, 𝑉𝐺𝑆
Using Taylor’s theorem by considering fractional change in 𝑉𝐷𝑆, 𝑉𝐺𝑆 & 𝐼𝐷
Δ𝐼𝐷 =
𝜕𝐼𝐷
𝜕𝑉𝐷𝑆 𝑉𝐺𝑆
Δ𝑉𝐷𝑆 +
𝜕𝐼𝐷
𝜕𝑉𝐺𝑆 𝑉𝐷𝑆
𝚫𝑽𝑮𝑺
Δ𝐼𝐷
𝚫𝑽𝑮𝑺
=
𝜕𝐼𝐷
𝜕𝑉𝐷𝑆 𝑉𝐺𝑆
Δ𝑉𝐷𝑆
𝚫𝑽𝑮𝑺
+
𝜕𝐼𝐷
𝜕𝑉𝐺𝑆 𝑉𝐷𝑆
If 𝐼𝐷 is constant,
Δ𝐼𝐷
Δ𝑉𝐺𝑆
= 0
0 =
𝛛𝑰𝑫
𝛛𝑽𝑫𝑺 𝑽𝑮𝑺
𝚫𝑽𝑫𝑺
𝚫𝑽𝑮𝑺
+
𝛛𝑰𝑫
𝛛𝑽𝑮𝑺 𝑽𝑫𝑺
𝒈𝒎 =
𝛛𝑰𝑫
𝛛𝑽𝑮𝑺 𝑽𝑫𝑺
𝒓𝒅 =
𝛛𝑽𝑫𝑺
𝛛𝑰𝑫 𝑽𝑮𝑺
𝝁 = −
𝛛𝑽𝑫𝑺
𝛛𝑽𝑮𝑺 𝑰𝑫
0 =
𝟏
𝒓𝒅
−𝝁 + 𝒈𝒎
𝜇
𝑟𝑑
= 𝑔𝑚
𝝁 = 𝒓𝒅 × 𝒈𝒎
𝒈𝒎 =
𝟐
𝑽𝑷
𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺
Show that
Decreasing the gate voltage
𝑉𝐺𝑆 from zero till 𝐼𝐷 is
reduced to zero
Characteristic is parabolic
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
= 1 −
𝑉𝐺𝑆
𝑉𝑃
2
𝑦 = 𝑥2
Shockley gives the equation of
drain characteristics as:
Equation of Parabola is given as
This resembles equation of
parabola
𝐼𝐷𝑆 = 𝐼𝐷𝑆𝑆 1 −
𝑉𝐺𝑆
𝑉𝑃
2
𝐼𝐷𝑆 = 𝐼𝐷𝑆𝑆 1 −
𝑉𝐺𝑆
𝑉𝑃
2
Differentiating above equation with
respect to 𝑉𝐺𝑆,
𝜕𝐼𝐷𝑆
𝜕𝑉𝐺𝑆
= 𝐼𝐷𝑆𝑆 × 2 1 −
𝑉𝐺𝑆
𝑉𝑃
−
1
𝑉𝑃
∵ 𝑔𝑚 =
𝜕𝐼𝐷𝑆
𝜕𝑉𝐺𝑆 𝑉𝐷𝑆
= −
2𝐼𝐷𝑆𝑆
𝑉𝑃
1 −
𝑉𝐺𝑆
𝑉𝑃
𝑔𝑚 = −
2𝐼𝐷𝑆𝑆
𝑉𝑃
𝟏 −
𝑽𝑮𝑺
𝑽𝑷
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
= 1 −
𝑉𝐺𝑆
𝑉𝑃
2
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
= 𝟏 −
𝑽𝑮𝑺
𝑽𝑷
∴ 𝑔𝑚 = −
2𝐼𝐷𝑆𝑆
𝑉𝑃
𝑰𝑫𝑺
𝑰𝑫𝑺𝑺
=
2
−𝑉𝑃
𝐼𝐷𝑆𝑆 × 𝐼𝐷𝑆
∴ 𝑔𝑚 =
2
−𝑉𝑃
𝑰𝑫𝑺𝑺
𝟐
× 𝑰𝑫𝑺
𝑰𝑫𝑺𝑺
𝒈𝒎 =
𝟐
𝑽𝑷
𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺
𝑔𝑚 = −
𝟐𝑰𝑫𝑺𝑺
𝑽𝑷
1 −
𝑉𝐺𝑆
𝑉𝑃
Let 𝑔𝑚 = 𝑔𝑚0 when 𝑉𝐺𝑆 = 0
𝑔𝑚0 = −
2𝐼𝐷𝑆𝑆
𝑉𝑃
1 −
0
𝑉𝑃
𝑔𝑚0 = −
𝟐𝑰𝑫𝑺𝑺
𝑽𝑷
𝑔𝑚 = 𝒈𝑚0 1 −
𝑉𝐺𝑆
𝑉𝑃
𝑔𝑚 = 𝒈𝑚0
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
= 1 −
𝑉𝐺𝑆
𝑉𝑃
2
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
= 1 −
𝑉𝐺𝑆
𝑉𝑃
∴ 𝑔𝑚 = −
2𝐼𝐷𝑆𝑆
𝑉𝑃
𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
=
2
−𝑉𝑃
𝐼𝐷𝑆𝑆 × 𝐼𝐷𝑆
∴ 𝑔𝑚 =
2
−𝑉𝑃
𝐼𝐷𝑆𝑆
2
× 𝐼𝐷𝑆
𝐼𝐷𝑆𝑆
𝒈𝒎 =
𝟐
𝑽𝑷
𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺

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ELECTRON DEVICES AND CIRCUITS ELECTRINICS AND EDC.pptx

  • 1. Unit – 6 Field Effect Transistor (FET) And MOSFET
  • 2. CONSTRUCTION OF JFET Figure 1: Symbol of n-channel FET Figure 2: Symbol of p-channel FET
  • 3. PRINCIPLE OF JFET (n-Channel) Drain characteristics of JFET
  • 4. PRINCIPLE OF JFET (n-Channel) Drain characteristics of JFET When 𝑽𝑮𝑺 = 𝟎 and 𝑽𝑫𝑺 = 𝟎 When 𝑽𝑫𝑺 = 𝟎 and 𝑽𝑮𝑺 is decreased from zero When 𝑽𝑮𝑺 = 𝟎 and 𝑽𝑫𝑺 is increased from zero When 𝑽𝑮𝑺 is negative and 𝑽𝑫𝑺 is increased
  • 5. CHARACTERISTICS PARAMETERS OF JFET 1. Mutual conductance or transconductance, 𝒈𝒎 𝑔𝑚 = 𝜕𝐼𝐷 𝜕𝑉𝐺𝑆 𝑉𝐷𝑆 = Δ𝐼𝐷 Δ𝑉𝐺𝑆 , 𝑤𝑖𝑡ℎ 𝑉𝐷𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 2. Drain resistance, 𝒓𝒅 𝑟𝑑 = 𝜕𝑉𝐷𝑆 𝜕𝐼𝐷 𝑉𝐺𝑆 = Δ𝑉𝐷𝑆 Δ𝐼𝐷 , 𝑤𝑖𝑡ℎ 𝑉𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 3. Drain conductance, 𝒈𝒅 𝑔𝑑 = 𝜕𝐼𝐷 𝜕𝑉𝐷𝑆 𝑉𝐺𝑆 = Δ𝐼𝐷 Δ𝑉𝐷𝑆 , 𝑤𝑖𝑡ℎ 𝑉𝐺𝑆 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 4. Amplification factor, 𝝁 𝜇 = − 𝜕𝑉𝐷𝑆 𝜕𝑉𝐺𝑆 𝐼𝐷 = − Δ𝑉𝐷𝑆 Δ𝑉𝐺𝑆 , 𝑤𝑖𝑡ℎ 𝐼𝐷 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
  • 6. Relationship among FET parameters or Relation between 𝝁, 𝒓𝒅 & 𝒈𝒎 𝐼𝐷 = 𝑓 𝑉𝐷𝑆, 𝑉𝐺𝑆 Using Taylor’s theorem by considering fractional change in 𝑉𝐷𝑆, 𝑉𝐺𝑆 & 𝐼𝐷 Δ𝐼𝐷 = 𝜕𝐼𝐷 𝜕𝑉𝐷𝑆 𝑉𝐺𝑆 Δ𝑉𝐷𝑆 + 𝜕𝐼𝐷 𝜕𝑉𝐺𝑆 𝑉𝐷𝑆 𝚫𝑽𝑮𝑺 Δ𝐼𝐷 𝚫𝑽𝑮𝑺 = 𝜕𝐼𝐷 𝜕𝑉𝐷𝑆 𝑉𝐺𝑆 Δ𝑉𝐷𝑆 𝚫𝑽𝑮𝑺 + 𝜕𝐼𝐷 𝜕𝑉𝐺𝑆 𝑉𝐷𝑆 If 𝐼𝐷 is constant, Δ𝐼𝐷 Δ𝑉𝐺𝑆 = 0 0 = 𝛛𝑰𝑫 𝛛𝑽𝑫𝑺 𝑽𝑮𝑺 𝚫𝑽𝑫𝑺 𝚫𝑽𝑮𝑺 + 𝛛𝑰𝑫 𝛛𝑽𝑮𝑺 𝑽𝑫𝑺 𝒈𝒎 = 𝛛𝑰𝑫 𝛛𝑽𝑮𝑺 𝑽𝑫𝑺 𝒓𝒅 = 𝛛𝑽𝑫𝑺 𝛛𝑰𝑫 𝑽𝑮𝑺 𝝁 = − 𝛛𝑽𝑫𝑺 𝛛𝑽𝑮𝑺 𝑰𝑫 0 = 𝟏 𝒓𝒅 −𝝁 + 𝒈𝒎 𝜇 𝑟𝑑 = 𝑔𝑚 𝝁 = 𝒓𝒅 × 𝒈𝒎
  • 7. 𝒈𝒎 = 𝟐 𝑽𝑷 𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺 Show that Decreasing the gate voltage 𝑉𝐺𝑆 from zero till 𝐼𝐷 is reduced to zero Characteristic is parabolic 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 1 − 𝑉𝐺𝑆 𝑉𝑃 2 𝑦 = 𝑥2 Shockley gives the equation of drain characteristics as: Equation of Parabola is given as This resembles equation of parabola 𝐼𝐷𝑆 = 𝐼𝐷𝑆𝑆 1 − 𝑉𝐺𝑆 𝑉𝑃 2
  • 8. 𝐼𝐷𝑆 = 𝐼𝐷𝑆𝑆 1 − 𝑉𝐺𝑆 𝑉𝑃 2 Differentiating above equation with respect to 𝑉𝐺𝑆, 𝜕𝐼𝐷𝑆 𝜕𝑉𝐺𝑆 = 𝐼𝐷𝑆𝑆 × 2 1 − 𝑉𝐺𝑆 𝑉𝑃 − 1 𝑉𝑃 ∵ 𝑔𝑚 = 𝜕𝐼𝐷𝑆 𝜕𝑉𝐺𝑆 𝑉𝐷𝑆 = − 2𝐼𝐷𝑆𝑆 𝑉𝑃 1 − 𝑉𝐺𝑆 𝑉𝑃 𝑔𝑚 = − 2𝐼𝐷𝑆𝑆 𝑉𝑃 𝟏 − 𝑽𝑮𝑺 𝑽𝑷 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 1 − 𝑉𝐺𝑆 𝑉𝑃 2 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 𝟏 − 𝑽𝑮𝑺 𝑽𝑷 ∴ 𝑔𝑚 = − 2𝐼𝐷𝑆𝑆 𝑉𝑃 𝑰𝑫𝑺 𝑰𝑫𝑺𝑺 = 2 −𝑉𝑃 𝐼𝐷𝑆𝑆 × 𝐼𝐷𝑆 ∴ 𝑔𝑚 = 2 −𝑉𝑃 𝑰𝑫𝑺𝑺 𝟐 × 𝑰𝑫𝑺 𝑰𝑫𝑺𝑺 𝒈𝒎 = 𝟐 𝑽𝑷 𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺
  • 9. 𝑔𝑚 = − 𝟐𝑰𝑫𝑺𝑺 𝑽𝑷 1 − 𝑉𝐺𝑆 𝑉𝑃 Let 𝑔𝑚 = 𝑔𝑚0 when 𝑉𝐺𝑆 = 0 𝑔𝑚0 = − 2𝐼𝐷𝑆𝑆 𝑉𝑃 1 − 0 𝑉𝑃 𝑔𝑚0 = − 𝟐𝑰𝑫𝑺𝑺 𝑽𝑷 𝑔𝑚 = 𝒈𝑚0 1 − 𝑉𝐺𝑆 𝑉𝑃 𝑔𝑚 = 𝒈𝑚0 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 1 − 𝑉𝐺𝑆 𝑉𝑃 2 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 1 − 𝑉𝐺𝑆 𝑉𝑃 ∴ 𝑔𝑚 = − 2𝐼𝐷𝑆𝑆 𝑉𝑃 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 = 2 −𝑉𝑃 𝐼𝐷𝑆𝑆 × 𝐼𝐷𝑆 ∴ 𝑔𝑚 = 2 −𝑉𝑃 𝐼𝐷𝑆𝑆 2 × 𝐼𝐷𝑆 𝐼𝐷𝑆𝑆 𝒈𝒎 = 𝟐 𝑽𝑷 𝑰𝑫𝑺 × 𝑰𝑫𝑺𝑺