For frequencies greater than 1 MHz the response of the transistor will be limited by internal and parasitic capacitance’s of the bipolar junction transistor. Hence at high frequencies the low frequency small signal model of transistor has to be modified to include the effects of internal and parasitic capacitance’s of bipolar junction transistor

• High frequency effects on BJT

The gain decreases at high frequencies due to internal feedback capacitance’s.The highest frequency of operation of BJT will be limited by internal capacitance’s of BJT.

The on and off switching times of BJT will be high and speed will be limited due to internal charge storage effects.

• High frequency model of BJT

The high frequency parameters of BJT may vary with operating point but the variation is negligible for small signal variations around the operating point. Following is the high frequency model of a transistor.

Where

$B^{\prime}$= internal node in base

$R_{bb^{\prime}}$ = Base spreading resistance

$R_{b^{\prime}e}$ = Internal base node to emitter resistance

$R_{ce}$ = collector to emitter resistance

$C_{e}$ = Diffusion capacitance of emitter base junction

$R_{b^{\prime}c}$ = Feedback resistance from internal base node to collector node

$g_{m}$ = Transconductance

$C_{C}$= transition or space charge capacitance of base collector junction.

$R{bb^{\prime}}$ is the base spreading resistance of BJT which represents the bulk resistance of the material between the base terminal and the physical inaccessible internal node of BJT. Typically it is of the order of 100’s of ohms.

$R_{b^{\prime}e}$ is the Internal base node to emitter resistance. It accounts for the increase recombination base current as emitter current increases. It is in parallel with the collector circuit and hence reduces the collector current value from emitter current.This resistance will be high order of kilo ohms as the decrease in the collector current due to base recombination currents will be very less.

$R_{b^{\prime}c}$ is the Feedback resistance from internal base node to collector node. It is included in the model to take in to account early effect.As collector to base reverse bias is increased(action) the effective width increases and collector current increases(feedback response).This feedback effect(early effect) is accounted for by Rb’c.

$R_{ce}$ represents the bulk resistance of the material between collector to emitter.

$C_{e}$ is the Diffusion capacitance of emitter base junction. Diffusion capacitance of emitter base junction is directly proportional to emitter bias current and forward base transit time. Forward transit time is defined as the average time the minority carrier spends in base. The Diffusion capacitance of emitter base junction accounts for the minority charge stored in base and is given as

$C_{e}=\tau_{F}^{\ast}I_{E}/V_{T}$

where IE is emitter bias current

$V_{T}$ is voltage equivalent of temperature = $k^{\ast}T/e$ =26 mV at 27 Deg C

$\tau_{F}$ is forward base transit time given as $\tau_{F} = W^{2}/(2 \ast D_{B})$

W is effective base width

$D_{B}$ is diffusion constant for minority carriers in base holes in PNP transistor and electrons in NPN transistor.

$C_{e}$ is a function of temperature as $DB = VT \ast μ$ (μ varies as $T^{m}$) is a function of temperature. $C_{e}$ can be found theoretically from unit gain frequency and Trans conductance as follows

$C_{e} = g_{m}/(2^{\ast} pi ^{\ast} f_{T})$

Unity gain frequency is defined as frequency at which the current gain of transistor reduces to unity. The 3 db higher cutoff frequency of BJT is termed as beta frequency of BJT denoted by $f_{\beta}$. The beta frequency and Unity gain frequency are related as

$f_{T} = h_{fe }\ast f_{ \beta}$

where $h_{fe}$ is current gain of BJT in CE configuration.

$C_{C}$ represents the transition or space charge capacitance of base collector junction.The transition capacitance of base collector junction is given as

$Cj = C_{o}/(1+V_{CB}/V_{BV})^{n}$

where $C_{o}$ is the transition capacitance for zero collector to base bias

$V_{CB}$ is collector to base bias

$V_{BV}$ is the built in voltage across base collector junction

n is a constant called as grading coefficient varies form 0.25 to 0.5.

The high frequency hybrid Pi or Giacoletto model of BJT is valid for frequencies less than the unit gain frequency