Stabilizing a Transistor
The scattering and noise parameters of a BJT at 4GHz are:
S11 = 0.65∠−95°
S12 = 0.035∠40°
S21 = 5∠115°
S22 = 0.8∠−35°
Show how resistive loading can stabilize the transistor.
Ref. Gonzalez, Microwave Transistor Amplifiers: Analysis and Design 2nd ed., Prentice Hall, example 3.3.2, p.226
this.push_element("ref=P1;val=1 Z0=50;x=112;y=128;rot=0;sx=1;sy=1;symbol=powersource")
this.push_element("ref=P2;val=1 Z0=50;x=352;y=128;rot=0;sx=1;sy=1;symbol=powersource")
this.push_element("ref=S1;val=BJT;x=232;y=136;rot=0;sx=1;sy=1;symbol=s2p_npn")
this.push_element("ref=*1;val=*;x=112;y=160;rot=0;sx=1;sy=1;symbol=gnd")
this.push_element("ref=.1;val=.SP LIN 1 0.8G 0.8G;x=112;y=200;rot=0;sx=1;sy=1;symbol=spice")
this.push_element("ref=*2;val=*;x=352;y=160;rot=0;sx=1;sy=1;symbol=gnd")
this.push_element("ref=.2;val=.MODEL BJT S2P ID=MODEL_S2P;x=112;y=216;rot=0;sx=1;sy=1;symbol=spice")
this.push_element("ref=*3;val=*;x=248;y=176;rot=0;sx=1;sy=1;symbol=gnd")
this.push_element("ref=R1;val=500;x=304;y=136;rot=90;sx=1;sy=1;symbol=resistor")
this.push_element("ref=*4;val=*;x=304;y=176;rot=0;sx=1;sy=1;symbol=gnd")
this.push_wire("ref=1;solder_start=false;solder_stop=false",[112,104,192,104,192,136,216,136])
this.push_wire("ref=2;solder_start=false;solder_stop=false",[248,104,352,104])
this.push_wire("ref=0;solder_start=false;solder_stop=false",[112,152,112,152])
this.push_wire("ref=0;solder_start=false;solder_stop=false",[352,152,352,152])
this.push_wire("ref=0;solder_start=false;solder_stop=false",[248,168,248,168])
this.push_wire("ref=2;solder_start=true;solder_stop=false",[304,104,304,112])
this.push_wire("ref=0;solder_start=false;solder_stop=false",[304,168,304,160])
s2p Model
Simulation Results
With R1=Infinity, the transistor is potentially unstable: K=0.547, |Δ|=0.504.
With R1=500Ω, the transistor becomes unconditionally stable: K=1.02, |Δ|=0.413.
Smaller R1 values result in more stable amplifiers at the cost of reduced power gains.
Re-simulation with