SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

8.8. SMALL AND LARGE SIGNAL ISSUES 415

is the frequency at which the power gain becomes unity, also called the power gain cut-off
frequency. In power amplifiers a load line match is usually provided at the output (equation
8.8.19) as in figure 8.40d, rather than a match for the maximum power gain as in figure 8.40c.
The large signal power gain (LSG) is then given by (for the caseRLRds),

LSG=

Pload

Pav,gen

=

(

Vbr−Vk

Vp

)

Gm

4 π^2 f^2 C^2 gsRi

≡

(

flsg

f

) 2

(8.8.13)

where

flsg=

√

Vbr−Vk

IDSS

fτ

√

Ri

(8.8.14)

Here the large signal power gain cut-off frequency (flsg) is the frequency at which the power
gain becomes unity for a load line match.
With the transistor parameters scaling with the device periphery (W)asIDSS∝W,Cgs∝
W,Gm∝W,Ri∝ 1 /WandRds∝ 1 /W,fτ,fmaxandflsgare independent of the device
periphery.

8.8.2 Power-frequency limit ...........................

An important limitation called the power-frequency (pf^2 ) limit relates to the inherent limit on
the breakdown voltage a high frequency device technology can achieve. This limits the output
power one can obtain from a given device technology. Thepf^2 limit, well-known in microwave
power transistor design, imposes particularly severe performance limits on broadband microwave
power amplifiers.
In high frequency transistors, whether HEMT or HBT, there is a high-field drift region separat-
ing the control region (the HEMT channel, the HBT base) from the output terminal. In HEMTs
it is the extension of the gate depletion region laterally toward the drain contact, while in a HBT
this drift region is the collector depletion layer. If the length of this region isDdrif t,andthe
semiconductor breakdown electric field isEmax, then the transistor breakdown voltage is,

Vbr=EmaxDdrif t (8.8.15)

This drift layer introduces space-charge transit time,τsct. If the electron velocity isvsat,then
the space charge transit time

τsct=

Ddrif t

2 vsat

(8.8.16)

and (ignoring all other transit delays) the unity current-gain cutoff frequency is

fτ≤

vsat

πDdrif t

(8.8.17)

Combining equation 8.8.15 and equation 8.8.17, we get

fτVbr≤

Emaxvsat

π

(8.8.18)