1. Small Signal High Frequency Transistor Amplifier Models
ENGI 242/ELEC 222
January 2004
UNIT II
Small Signal High Frequency Transistor Amplifier Models
BJT Small Signal Model

2. HYBRID MODEL PI

3. HYBRID MODEL PI PARAMETERS
Parasitic Resistances
rb = rb’b = ohmic resistance – voltage drop in base region caused by transverse flow of majority carriers, 50 ≤ rb ≤ 500
rc = rce = collector emitter resistance – change in Ic due to change in Vc, 20 ≤ rc ≤ 500
rex = emitter lead resistance
important if IC very large, 1 ≤ rex ≤ 3

4. HYBRID MODEL PI PARAMETERS
Parasitic Capacitances
Cje0 = Base-emitter junction (depletion layer) capacitance, 0.1pF ≤ Cje0 ≤ 1pF
C0 = Base-collector junction capacitance, 0.2pF ≤ C0 ≤ 1pF
Ccs0 = Collector-substrate capacitance, 1pF ≤ Ccs0 ≤ 3pF
Cje = 2Cje0 (typical)
0 =.55V (typical)
F = Forward transit time of minority carriers, average of lifetime of holes and electrons, 0ps ≤ F ≤ 530ps

5. HYBRID MODEL PI PARAMETERS
r = rb’e = dynamic emitter resistance – magnitude varies to give correct low frequency value of Vb’e for Ib
r = rb’c = collector base resistance – accounts for change in recombination component of Ib due to change in Vc which causes a change in base storage
c = Cb’e = dynamic emitter capacitance – due to Vb’e stored charge
c = Cb’c = collector base transistion capacitance (CTC) plus Diffusion capacitance (Cd) due to base width modulation
gmV = gmVb’e = Ic – equivalent current generator

6. Hybrid Pi Relationships
 = gm r
January 2004
ENGI 242/ELEC 222

7. Hybrid Pi Relationships

8. HYBRID MODEL PI MID BAND

9. HYBRID MODEL PI HIGH FREQ.

10. Common Emitter Amplifier - Complete Hybrid PI

11. Mid Band Hybrid PI Common Emitter

12. Equivalent Circuit to find ZO

13. High Frequency Hybrid PI CE Amp

19. Current Gain with Resistive Load

21. Gain Bandwidth Product
For transistors, the current-gain–bandwidth product is known as the fT or transition frequency. 
It is calculated from the low-frequency (a few KHz) current gain under specified test conditions, and the cutoff frequency at which the current gain drops by 3 decibels (70% amplitude); the product of these two values can be thought of as the frequency at which the current gain would drop to 1, and the transistor current gain between the cutoff and transition frequency can be estimated by dividing fT by the frequency.
Usually, transistors must be applied at frequencies well below fT to be useful as amplifiers and oscillators. In a bipolar junction transistor, frequency response declines owing to the internal capacitance of the junctions. The transition frequency varies with collector current, reaching a maximum for some value and declining for greater or lesser collector current.