Electronics Formula Sheet
2
β Over drive Voltage: = ( β ) β β² = (/ 2 ) β Cut off ( =0): < ; β Channel induced and Mosfet is in triode or saturation: = + Stats Triode region Saturation Region Conditions > < β€ β₯ 1 2 β² ( β 1 2 ) 1 2 β² 2 β = = β² = = β2 β² β β( ) = 2 (4.6.2,6), β = 1 , β = | | , β = β ( || ), Characteristic Parameters MOSFET Voltage Gain, Input Resistance, Output Resistance, Common Source (Hybrid model) β ( || || ) β + ( || || ) β || Common Source with a source resistance (T-Model) β ( || ) 1+ β + ( || ) 1+ β Common Gate (T-Model) ( || ) 1 1+ ( || ) 1 Common Drain (T-Model) || ( || )+ 1 + . || ( || )+ 1 β 1 β = 2( + ) (Unity Gain Frequency) β β² = || || β = (1 + β² ) β = + , β = 1 2 ( || ) (Upper 3-dB freq.) Differential and multi-stage amplifier Let I be the total current in common mode voltage β 1 = 2 = β 2 , β 1 = 2 = 2 = β² 2 The value of at which the entire bias current I is steered into Q1 is = 1 + = β2 Output of differential pair taken single ended: β Common-mode gain = | |= 2 , β Differential gain = | |= 1 2 , β CMMR=| |= Output of differential pair taken differentially: β Common-mode gain = | |=0 , β Differential gain = | |= , β CMMR=| |=β Mismatch effect ( ) : β =β β 2 (Rd mismatch), β CMMR=| | = 2 /( β ),β = 2 β ( β), β CMMR=| |= 2 /( β ) Electronics II Formula Sheet by Haris H.
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Transcript of Electronics Formula Sheet
β Over drive Voltage: πππ = (ππΊπ β ππ‘) β πβ²π = πππΆππ₯ (π΄/π2)
β Cut off (ππ· = 0): π£πΊπ < ππ‘π; β Channel induced and Mosfet is in triode or saturation: π£πΊπ = π£π‘π + π£ππ
Stats Triode region Saturation Region
Conditions π£πΊπ· > ππ‘
π£π·π < π£ππ π£πΊπ· β€ ππ‘
π£π·π β₯ π£ππ
ππ· 1
2πβ²
π
π
πΏ(π£ππ β
1
2π£π·π)π£π·π
1
2πβ²
π
π
πΏπ£ππ
2
β ππ =ππ
π£ππ = πβ²
π π
πΏπππ = ππ = β2πΎπ
β² βπΌπ·β(π
πΏ) =
2πΌπ·
πππ(4.6.2,6), β ππ΄ =
1
π , β ππ =
|ππ΄|
πΌπ· , β π΄π£ = βππ(π π·||ππ),
Characteristic Parameters
MOSFET Voltage Gain, π΄π£ πΊπ£ Input
Resistance,π π Output
Resistance,π π
Common Source (Hybrid model)
βππ(π π·||ππ||π π) βπ πΊ
π πΊ + π π ππππ(π π·||ππ||π π) β π π·||ππ
Common Source with a source resistance
(T-Model)
βππ(π π·||π π)
1 + πππ π β
π πΊ
π πΊ + π π ππ
ππ(π π·||π π)
1 + πππ π β π π·
Common Gate (T-Model)
ππ(π π·||π π) 1
1 + πππ π ππππ(π π·||π π)
1
ππ π π·
Common Drain (T-Model)
ππ||π π
(ππ||π π) +1
ππ
π πΊ
π πΊ + π π ππ.
ππ||π π
(ππ||π π) +1
ππ
β 1
ππ
β ππ‘ =ππ
2π(πΆππ +πΆππ)(Unity Gain Frequency) β π πΏ
β² = π π·||ππ||π πΏ β πΆππ = πΆππ(1 + πππ πΏβ² ) β πΆππ = πΆππ + πΆππ,
β ππ» =1
2ππΆππ(π π ππ||π πΊ)(Upper 3-dB freq.)
Differential and multi-stage amplifier
Let I be the total current in common mode voltage
βπ£π·1 = π£π·2 = ππ·π· βπΌ
2π π·, β ππ·1 = ππ·2 =
πΌ
2= πβ²
π π
πΏπ£ππ
2
The value of π£ππ at which the entire bias current I is steered into Q1 is π£πππππ₯ = π£πΊπ1 + π£π = β2πππ
Output of differential pair taken single ended:
β Common-mode gain = |π΄πΆπ| =π π·
2π π π , β Differential gain = |π΄π| =
1
2πππ π·, β CMMR=|
π΄π
π΄πΆπ| = πππ π π
Output of differential pair taken differentially:
β Common-mode gain = |π΄πΆπ| = 0 , β Differential gain = |π΄π| = πππ π·, β CMMR=|π΄π
π΄πΆπ| = β
Mismatch effect (ππ πππ π π·) :
βπ΄πΆπ = ββπ π·
2π π π (Rd mismatch), β CMMR=|
π΄π
π΄πΆπ| = 2πππ π π /(
βπ π·
π π·),β π΄πΆπ =
π π·
2π π π
βππ
ππ( πππππ πππ‘πβ), β CMMR=|
π΄π
π΄πΆπ| =
2πππ π π /(βππ
ππ)
Electronics II Formula Sheet by Haris H.
OP-AMP Configuration and their Outputs
