Why we need to know ft and fmax of a device?
But why we need both two parameters? why we need fmax in addition to
ft?
2)a simple formula, if we want the rf amplifier with higher realiability, the ft
of device should be larger than 10*operating frequency.
Any similar formula for fmax like this?
ft comes from the early days where devices were expensive. The ft was a figure of merit to help engineers select the valve or transistor for their broad band (video) or tuned (RF or IF stages) amplifiers. It was a good predictor of lower frequency performance where there was reasonable ( 20 dB or more) gain.
In operating at the higher frequencies a better figure of merit was needed where gains of 6 dB were acceptable.
ft , the unit gain frequncy where the current gain of the device is unity
fmax the unit power gain , where the power gain is unity
fmax : indicate the max oscillation frequncy of the device
khouly
How we apply them, ft and fmax, in RF design such as LNA or PA?
ft is usually given at specific operation current. It is the frequency where the modulus of the Short circuit current gain is 1:
For a BJT
Knowing the ft of the device at specific operation current and the hfe(dc current gain) u can deduce parameters of the device like Rbe, Ct=Cbe+Cbc and Fb(-3db). You can also predict S21 which is fairly accurate for frequency<Fb. With that in knowledge u can have preliminary design in a spread sheet that u can apply in a Simulation program to fine tune it.
Let me give an Example for a BJT CE Configuration:
lets say Ft=5Ghz Hfe=100 Ic=10mA feedBack Cap Cbc=1pf and Rbb=10 Ohm (all that usually given in a datasheet)
There fore:
Re=Vt/Ic=2.5 Ohm <-- AC resistance
Thus Rbe=(b+1)Re= 250Ohm
also Ct*Rbe=1/2*pi*fb
from that u can calcualte Ct*Rbe and Ct=12.6Pf
and deduce what is Cbe=11.6pf
From there U can go to your Ebers Pi model with finite load impedance (not short circuit) and finite input source impedance. Using the miller effect find the real Ct and Rin including Rs. And find the F3db for your amplifier.
CT=(1+gm*RL)*Cbc+Cbe=32.6pf
Rin now is =(Rbb+Rs)*Rbe)/(Rbb+Rs+Rbe)
and F3db=1/(2*pi*Rin*CT)=101Mhz
from there u use that
S21=2(gm*RL)*(Rbe/(Rbe+Rbb+Rs)=32.25 that is for low Frequencies
For high u need to include the roll off 20db/dec multipling the above equation by (1/1+j W*CT*Rin)
If u want to be more accurate u can include in series with Re the emiter fixed resistance about 1 ohm and find egain the above parameters, that will give u a better result which is quite close with S param measurements file u get for a specific transistor.