LC oscillator design (GP)
Vdd = 1.2;
CL = 0.2e-12;
F = 5e9;
omega = 2*pi*F;
FOff = 6e5;
LoopGainSpec = 2.0;
Vbias = 0.2;
T = 0.1;
CvarRatio = 3;
CswBits = 3;
CswSegs = 2^(CswBits);
CvarCswLSBOverlap = 2;
cvxq = cvx_quiet(true);
disp('Generating the optimal tradeoff curve...')
powers = [];
for PNSpec=0.7e-12:0.2e-12:1e-11
cvx_begin gp
variable D;
variable W;
variable SRF;
variable l;
variable w;
variable I;
variable VOsc;
variable CT;
variable Csw;
variable Cvar;
variable IBias;
variable CMaxFreq;
minimize( Vdd*IBias )
subject to
SRFSpec = 3*F;
omegaSRF = 2*pi*SRF;
L = 2.1e-06*D^(1.28)*(W)^(-0.25)*(F)^(-0.01);
R = 0.1*D/W+3e-6*D*W^(-0.84)*F^(0.5)+5e-9*D*W^(-0.76)*F^(0.75)+0.02*D*W*F;
C = 1e-11*D+5e-6*D*W;
Area = (D+W)^2;
G = R/(omega*L)^2;
invQ = R/(omega*L);
Area <= 0.25e-6;
W <= 30e-6;
5e-6 <= W;
10*W <= D;
D <= 100*W;
SRFSpec <= SRF;
omegaSRF^2*L*C <= 1;
GM = 6e-3*(w/l)^0.6*(I/2)^(0.4);
GD = 4e-10*(w/l)^0.4*(I/2)^(0.6)*1/l;
Vgs = 0.34+1e-8/l+800*(I*l/(2*w))^0.7;
Cgs = 1e-2*w*l;
Cgd = 1e-9*w;
Cdb = 1e-9*w;
2e-6 <= w;
0.13e-6 <= l;
l <= 1e-6;
invVOsc = (G+GD)/IBias;
kT4 = 4*1.38e-23*300;
kT4G = 2*kT4;
LoopCurrentNoise = kT4*G;
TransistorCurrentNoise = 0.5*kT4G*GM;
PN = 1/(160*(FOff*VOsc*CT)^2)*(LoopCurrentNoise+TransistorCurrentNoise);
Cfix = C+0.5*(CL+Cgs+Cdb+4*Cgd);
CDiffMaxFreq = Cfix+0.5*Cvar;
invLoopGain = (G+0.5*GD)/(0.5*GM);
PN <= PNSpec;
omega^2*L*CT == 1;
omega^2*(1+T)^2*L*CMaxFreq == 1;
4*T/((1-T^2)^2)*CT <= Csw*(1+CvarCswLSBOverlap/CswSegs);
Csw*CvarCswLSBOverlap/CswSegs <= 0.5*Cvar*(CvarRatio-1);
CDiffMaxFreq <= CMaxFreq;
VOsc+2*Vbias <= 2*Vdd;
VOsc*invVOsc <= 1;
invLoopGain*LoopGainSpec <= 1;
Vbias+Vgs+IBias/2*R/2 <= Vdd;
I == IBias;
cvx_end
fprintf(1,' PNSpec = %5.2f (dBc/Hz) min_power = %3.2f (mW)\n', ...
10*log10(PNSpec),cvx_optval/1e-3);
powers = [powers cvx_optval];
end
PNSpec = [0.7e-12:0.2e-12:1e-11];
plot(10*log10(PNSpec),powers/1e-3);
xlabel('Phase Noise (dBc/Hz)')
ylabel('Power (mW)')
disp('Optimal tradeoff curve plotted.')
cvx_quiet(cvxq);
Generating the optimal tradeoff curve...
PNSpec = -121.55 (dBc/Hz) min_power = 19.14 (mW)
PNSpec = -120.46 (dBc/Hz) min_power = 11.45 (mW)
PNSpec = -119.59 (dBc/Hz) min_power = 8.38 (mW)
PNSpec = -118.86 (dBc/Hz) min_power = 6.47 (mW)
PNSpec = -118.24 (dBc/Hz) min_power = 5.65 (mW)
PNSpec = -117.70 (dBc/Hz) min_power = 5.31 (mW)
PNSpec = -117.21 (dBc/Hz) min_power = 5.03 (mW)
PNSpec = -116.78 (dBc/Hz) min_power = 4.78 (mW)
PNSpec = -116.38 (dBc/Hz) min_power = 4.57 (mW)
PNSpec = -116.02 (dBc/Hz) min_power = 4.39 (mW)
PNSpec = -115.69 (dBc/Hz) min_power = 4.22 (mW)
PNSpec = -115.38 (dBc/Hz) min_power = 4.07 (mW)
PNSpec = -115.09 (dBc/Hz) min_power = 3.94 (mW)
PNSpec = -114.81 (dBc/Hz) min_power = 3.82 (mW)
PNSpec = -114.56 (dBc/Hz) min_power = 3.71 (mW)
PNSpec = -114.32 (dBc/Hz) min_power = 3.61 (mW)
PNSpec = -114.09 (dBc/Hz) min_power = 3.52 (mW)
PNSpec = -113.87 (dBc/Hz) min_power = 3.43 (mW)
PNSpec = -113.67 (dBc/Hz) min_power = 3.35 (mW)
PNSpec = -113.47 (dBc/Hz) min_power = 3.27 (mW)
PNSpec = -113.28 (dBc/Hz) min_power = 3.20 (mW)
PNSpec = -113.10 (dBc/Hz) min_power = 3.14 (mW)
PNSpec = -112.92 (dBc/Hz) min_power = 3.08 (mW)
PNSpec = -112.76 (dBc/Hz) min_power = 3.02 (mW)
PNSpec = -112.60 (dBc/Hz) min_power = 2.96 (mW)
PNSpec = -112.44 (dBc/Hz) min_power = 2.91 (mW)
PNSpec = -112.29 (dBc/Hz) min_power = 2.86 (mW)
PNSpec = -112.15 (dBc/Hz) min_power = 2.82 (mW)
PNSpec = -112.01 (dBc/Hz) min_power = 2.77 (mW)
PNSpec = -111.87 (dBc/Hz) min_power = 2.73 (mW)
PNSpec = -111.74 (dBc/Hz) min_power = 2.69 (mW)
PNSpec = -111.61 (dBc/Hz) min_power = 2.65 (mW)
PNSpec = -111.49 (dBc/Hz) min_power = 2.61 (mW)
PNSpec = -111.37 (dBc/Hz) min_power = 2.58 (mW)
PNSpec = -111.25 (dBc/Hz) min_power = 2.54 (mW)
PNSpec = -111.14 (dBc/Hz) min_power = 2.51 (mW)
PNSpec = -111.02 (dBc/Hz) min_power = 2.48 (mW)
PNSpec = -110.92 (dBc/Hz) min_power = 2.45 (mW)
PNSpec = -110.81 (dBc/Hz) min_power = 2.42 (mW)
PNSpec = -110.71 (dBc/Hz) min_power = 2.39 (mW)
PNSpec = -110.60 (dBc/Hz) min_power = 2.36 (mW)
PNSpec = -110.51 (dBc/Hz) min_power = 2.33 (mW)
PNSpec = -110.41 (dBc/Hz) min_power = 2.31 (mW)
PNSpec = -110.32 (dBc/Hz) min_power = 2.28 (mW)
PNSpec = -110.22 (dBc/Hz) min_power = 2.26 (mW)
PNSpec = -110.13 (dBc/Hz) min_power = 2.24 (mW)
PNSpec = -110.04 (dBc/Hz) min_power = 2.21 (mW)
Optimal tradeoff curve plotted.