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

HYBRID MODEL PI

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

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

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

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

Hybrid Pi Relationships

HYBRID MODEL PI MID BAND

HYBRID MODEL PI HIGH FREQ.

Common Emitter Amplifier - Complete Hybrid PI

Mid Band Hybrid PI Common Emitter

Equivalent Circuit to find ZO

High Frequency Hybrid PI CE Amp

Current Gain with Resistive Load

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.