Design for a minimum noise figure

The scattering and noise parameters of a BJT at 4GHz are:

S11=0.552 ∠169° S12=0.049 ∠23° S21=1.681 ∠26° S22=0.839 ∠−67° Fmin=2.5dB Γopt=0.475∠166° Rn=3.5Ω

Design a microwave transistor amplifier to achieve a minimum noise figure.

Ref. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design 2nd ed., Prentice Hall, example 4.3.1, p.302

s2p Model

# GHz S MA R 50 ! f S11 S21 S12 S22 ! GHz MAG ANG MAG ANG MAG ANG MAG ANG 4.0 0.552 169 1.681 26 0.049 23 0.839 -67 ! f Fmin Gammaopt Rn/50 ! GHz dB MAG ANG - 4.0 2.5 0.475 166 0.07

Simulation Results

Rollet stability factor K=1.01, |Δ|=0.419
→ This transistor is unconditionally stable at 4GHz.
→ Maximum available gain (MAG)=14.7dB

Maximum available power gain Gamax is obtained with Γs = 0.941∠−154°
Minimum noise figure (NF) is obtained with Γs = Γopt = 0.475∠166°
For the minimum NF, the input matching network should be designed such that Γs = Γopt. The available power gain is reduced to Ga=11dB.

Assuming Γs = Γopt, the reflection coeffficient looking into the collector becomes :
Γout = S22+(S12*S21*Γs)/(1−S11*Γs)
The output matching network should be conjugate-matched to Γout:  Γ_L = Γout^* = 0.844∠70.4°

The above Smith chart also shows the maximum operating power gain point:  Γ_L for Gpmax=0.979∠70.4°, which is calculated under the assumption that Γs is chosen to have the maximum available power gain. So this Γ_L is slightly different from that for the minimum noise figure.