Know about the need of DC Load line and stability factor for fixed biasing circuit

1. DC LOAD LINE
STABILIZATION TECHNIQUES
Dr.N.G.Praveena
Associate Professor/ECE
R.M.K. COLLEGE OF ENGINEERING
AND TECHNOLOGY

2. DC LOAD LINE
 Used to determine the collector current at any
desired collector-emitter voltage.
 For dc analysis no input ac signal is applied.

3.  For dc analysis
1. Remove Vin
2. Cc are coupling capacitors – (xc= 1/2πfc)
since f =0; open circuit

4.  Apply KVL to the collector
𝑽𝒄𝒄 = 𝑰𝒄𝑹𝒄 + 𝑽𝑪𝑬
𝑰𝒄𝑹𝒄 = - 𝑽𝑪𝑬 + 𝑽𝒄𝒄
𝑰𝒄 = - ( 1/𝑹𝒄 ) 𝑽𝑪𝑬 + ( 1/𝑹𝒄 ) 𝑽𝒄𝒄 - - - (1)
On comparing equation 1 with the straight line
equation y = mx +c, Where m = - (1/ Rc)
 Apply KVL to the Base
𝑽𝒄𝒄 = 𝑰𝑩𝑹𝑩 + 𝑽𝑩𝑬
𝑰𝑩𝑹𝑩 = 𝑽𝒄𝒄 - 𝑽𝑩𝑬
𝑰𝑩𝑸 = 𝑰𝑩 =
𝑽𝒄𝒄 − 𝑽𝑩𝑬
𝑹𝑩

6. x,y coordinates
 Point A : 𝑰𝒄 = - ( 1/𝑹𝒄 ) 𝑽𝑪𝑬 + ( 1/𝑹𝒄 ) 𝑽𝒄𝒄 - - - (1)
To find y coordinate sub 𝑽𝑪𝑬 = 0 in eqn (1)
𝑰𝒄 = ( 1/𝑹𝒄 ) 𝑽𝒄𝒄
Hence Point A : ( 0 , 𝑽𝒄𝒄 / 𝑹𝒄 )
 Point B:
To find x coordinate sub 𝑰𝒄 = 0 in eqn (1)
0 = - ( 1/𝑹𝒄 ) 𝑽𝑪𝑬 + ( 1/𝑹𝒄 ) 𝑽𝒄𝒄
𝑽𝑪𝑬 = 𝑽𝒄𝒄
Hence Point B : (𝑽𝒄𝒄 , 0)

7. VARIATION OF Q POINT
 Reverse saturation current, 𝑰𝑪𝑶 which
doubles for every 10˚C increase in
temperature.
 Base-emitter voltage, 𝑽𝑩𝑬 which decreases
by 2.5 mV per ˚ C.
 Transistor current gain, β, which increases
with temperature.

8. HOW TO MAKE Q POINT STABLE
STABILIZATION COMPENSATION
TECHNIQUE TECHNIQUE

9. STABILIZATION TECHNIQUE
 Use of resistive biasing circuits which allow IB to
vary so as to keep IC relatively constant with
variations in ICBO, β and VBE.
 Fixed Bias (or) Base resistor method
 Collector-to-Base bias (or) Biasing with feedback
resistor
 Voltage-divider bias (or) Self bias (or) Emitter bias

10. COMPENSATION TECHNIQUE
 Use of temperature sensitive devices such as
diodes, sensistors, thermistors which provide
compensating voltage and currents to maintain the
operating point constant.
 Diode Compensation
 Sensistor Compensation
 Thermistor Compensation

11. STABILIZATION TECHNIQUE
 How to validate these techniques???
Stability factors
S , S′, S′′

12. Stability Factor (S)
The rate of change of collector current IC with
respect to the collector base leakage current ICO,
keeping both the current IB and the current gain β
constant.
S =
𝝏𝑰𝑪
𝝏𝑰𝑪𝑶
, β and 𝑽𝑩𝑬 constant

13. Stability factor S′
The rate of change of IC with VBE, keeping ICO and β
constant.
S′ =
𝝏𝑰𝑪
𝝏𝑽𝑩𝑬
, β and 𝑰𝑪𝑶 constant

14. Stability factor S′′
The rate of change of IC with respect to β, keeping
ICO and VBE constant.
S′′ =
𝝏𝑰𝑪
𝝏β
, 𝑰𝑪𝑶 and 𝑽𝑩𝑬 constant

15. STEPS TO DETERMINE 3S
STEP 1 :
OBTAIN AN EXPRESSION FOR IB
STEP 2:
TO OBTAIN S, DIFFERENTIATE IB WITH RESPECT TO IC
AND SUBSITUTE IN THE STANDARD EQUATION OF S
STEP 3:
TO OBTAIN S′ REPLACE IB INTERMS OF VBE IN THE
STANDARD EQUATION OF IC AND DIFFERENTIATE IT
WITH REPECT TO VBE
STEP 4 :
TO OBTAIN S′′ DIFFERENTIATE THE EQUATION
OBTAINED IN STEP 3 WITH REPSPECT TO β

16. STANDARD EQUATION OF IC
 The collector current for a CE amplifier is given by
𝑰𝑪 = β 𝑰𝑩 + (1 + β) 𝑰𝑪𝑶
 Differentiating the above equation with respect to IC,
we get
1 = β ∂ 𝑰𝑩 / ∂ 𝑰𝑪 + ( 1 + β ) ∂ 𝑰𝑪𝑶 / ∂ 𝑰𝑪
 Therefore,
1 – β ∂ 𝑰𝑩 / ∂ 𝑰𝑪 = (1 + β) / S
S =
(1 + β)
1 – β ∂ 𝑰𝑩 / ∂ 𝑰𝑪
 From this equation, it is clear that this factor S should
be as small as possible to have better thermal
stability.

17. Fixed Bias
 Biasing voltage VCC,
VBE, RB and RC are
constant quantities.
 IB remains fixed at a
particular level. It is
called fixed biasing.
Resistance RB is selected to obtain the desired
level of IB.

18.  For dc analysis
ac input signal = 0
C1 and C2 – open circuit (∵f = 0)

19. STEP 1 :OBTAIN AN EXPRESSION
FOR IB
 Apply KVL to the base
𝑉𝐶𝐶 = 𝑰𝑩𝑹𝑩 + 𝑽𝑩𝑬
𝑰𝑩 =
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
--- (1)

20. STEP 2: TO OBTIAN S , DIFFERENTIATE IB WITH
RESPECT TO IC AND SUBSITUTE IN THE
STANDARD EQUATION OF S
Differentiate eqn (1) with respect to Ic
𝝏𝑰𝑩
𝝏𝑰𝑪
= 0 --- (2)
We know that the standard equation of S is
S =
(1 + β)
1 – β ∂ 𝑰𝑩 / ∂ 𝑰𝑪
---(3)
Sub (2) in (3)
S = (1 + β )
𝑰𝑩 =
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
--- (1)

21. STEP 3: TO OBTAIN S′, REPLACE IB INTERMS OF
VBE IN THE STANDARD EQUATION OF IC AND
DIFFERENTIATE IT WITH RESPECT TO VBE
The Standard Equation of Ic is
𝑰𝑪 = β𝑰𝑩 + (1+β) 𝑰𝑪𝑶
Sub (1)
𝑰𝑪 = β
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
(∵ 𝑰𝑪𝑶 <<) - - -(4)
Differentiate eqn(4)with respect to VBE
𝝏𝑰𝑪
𝝏𝑽𝑩𝑬
= -
𝜷
𝑹𝑩
∴ S′ =
𝝏𝑰𝑪
𝝏𝑽𝑩𝑬
= -
𝜷
𝑹𝑩
𝑰𝑩 =
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
--- (1)

22. STEP 4 : TO OBTAIN S′′ DIFFERENTIATE THE
EQUATION OBTAINED IN STEP 3 WITH
REPSPECT TO β
 Differentiate eqn (4) with respect to β
𝑰𝑪 = β
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
- - -(4)
𝝏𝑰𝑪
𝝏β
=
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
∴ S′′ =
𝑽𝑪𝑪 −𝑽𝑩𝑬
𝑹𝑩
= 𝐈𝑩 USING (1)