Mumbai University > EXTC > Sem 3 > Analog Electronics 1

Marks: 4 M

Year: May 2014

• Hybrid $π$ model is used mostly at high frequency because it provides more accurate result than other two models($r_e$ model and hybrid equivalent model) $\$
• It takes stray parasitic capacitance effect it appears between various junctions of the device. This effect comes into play only at high frequency for low to mid frequency the reactance is very large and hence can be considered as open circuit.

Fig1 Full hybrid π model of BJT

• Capacitance $C_u$ represents the transition or space charge capacitance of base collector junction and Capacitance $C_π$ 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. Values of both the capacitors are in the range of picofarad.

• $r_B$ is base spreading resistance which represents the bulk resistance of the material between the base terminal and the physical inaccessible internal node of BJT. $r_π$ is Internal base node to emitter resistance it accounts for the increase recombination base current as emitter current increases $r_u$ is Feedback resistance from internal base node to collector node it is included in the model to take in to account early effect.ro is collector to emitter resistance represents the resistance of the material between collector to emitter. $R_C$ is load resistance

• High frequency model parameters of a BJT in terms of low frequency hybrid parameters is given below

  1.Transconductance $g_m = I_c/V_T$

  $I_c$ is the quiescent collector current (also called the collector bias or DC collector current)

  $V_T =\frac{kT}{q}$is the thermal voltage calculated at approximately room temperature $(295K, 22°C or 71°F)$

  2.$r_π=\frac{V_T}{I_B}$

  3.$rO=\frac{V_A +V_{CE}}{I_C}$ , where $V_A$=early voltage

• Early effect is the variation of collector-base depletion region width due to variation in applied

Fig1 (a) diode in normal condition (b) early effect

• At low collector-base voltage the width of collector-base depletion region is relatively smaller than the active base (emitter-base )depletion region as shown in Fig1(a)
• At high collector-base voltage the width of collector-base depletion region is much larger than the active base (emitter-base) depletion region also area under base region decreases as shown in Fig1(b) This is known as early effect.