Three Transistor Biasing

Fixed biased

Input section
Applying kirchoff's vltage law to input side

Vcc=IbRb+Vbe

Ib=(Vcc-Vbe)/Rb

but Vbe<<Vce => Ib=Vcc/Rb

thus for fixed Vcc&Rb , the base current is fixed ,hence collector fixed bias

Output section
Applying Kirchoff's voltage law to output side

Vcc=IcRc+Vce

Vce=Vcc-IcRc

Ic=βIb+(1+β)Icbo
Ic=βIb+Iceo

Iceo=== leakage current
βIb===contribution of input current
β===Current gain

Iceo=(1+β)Icbo

for an ideal contains
Ic=βIb
Stability factor
 \( \left . Ic =  β{\frac{V_{CC}}{R_B}}+(1+β)Icbo\right . \)
differentiating with respect \[I_{icbo}\]
       \( \left . s =  β{\frac{dI_{C}}{dI_{cbo}}} = β+1 \right . \)


Reason why fixed bias is never used 
Any rise in temperature results in rise in Icbo and Iceo ,Hence collector current Ic rises resulting in rise in collector junction temperature , this is a cumulative process and collector current goes on increasing


Collector to base bias 

Input section
Applying kvl to input side

Vcc=(Ic+Ib)Rc+IbRb+Vbe

Ib=[(Vcc-IcRc)-Vbe]/(Rc+Rb)

Output section
applying kvl to output side

Vcc=(Ic+Ib)Rc+Vce

since Ib<<Ic

=> Vce=Vcc-IcRc

Ib=(Vce-Vbe)/(Rc+Rb)

As temperature increase ,leakage current Iceo rises

Ic=(βIb+Iceo)↑
Vce=Vcc-IcRc ↓

It will decrease Ib also .This will result in reduced Ic so this stabilise operating point

Self bias /Emitter bias /Voltage divider bias/potential divider bias

Vb=VccR2/(R1+R2)
Rb=R1||R2











This biasing method is most popularly used because it provide excellent operating point  stability ,When temperature increases ,leakage current increases ,thus voltage across Re increases, This will reverse bias the base emitter junction ,But R1-R2 combination across Vcc produces a positive voltage Vb at the base relative to emitter

Rb=R1R2/(R1+R2)
Vb=VccR2/(R1+R2)

applying kvl in output side

Vcc=IcRc+Vce+(Ic+Ib)Re

Ve=(Ic+Ib)Re

Vbe=Vb-Ve

Ic=βIb+Iceo

Stabilization 
Any rise in temperature T, cause a rise in Icbo and hence rise in Ic .This increased current through Re cause increase in DC voltage drop across Re and reduces te E-B forward bias , reducing the base current and thus collector current Ic. This reduction in Ic tends to cancel the rise in Ic cause by temperature rise . and thus operating point stability is improved