% Boyd, Kim, and Mohan, "Geometric programming and its
% applications to EDA Problems", (DATE Tutorial 2005), pp.102-113.
% Original code by S. Mohan
% Written for CVX by Almir Mutapcic 02/08/06
%
% Designs an LC oscillator consisting of a loop inductor, varactors
% for fine tuning, binary weighted switching capacitors for coarse
% tuning, cross coupled NMOS transistors, and tail current source.
% The optimal LC oscillator design iwith minimum power consumption,
% and limits on phase noise, area, etc... can be formulated as a GP:
%
%   minimize   P
%       s.t.   N <= Nmax, A <= Amax, l >= lmin, etc.
%
% where optimization variables are loop inductor dimensions D,W,
% size of varactor Vc, size of switching caps Csw, width and length
% of transistors Wnmos, Lnmos, bias current Ibias, etc.

%********************************************************************
% problem data
%********************************************************************
Vdd   = 1.2;         % voltage
CL    = 0.2e-12;     % load capcitance
F     = 5e9;         % operating frequency in Hz
omega = 2*pi*F;      % operating freq. in radians

FOff   = 6e5;        % offset frequency for phase noise calculation
LoopGainSpec = 2.0;  % loop gain spec
Vbias  = 0.2;        % non ideality of current mirror

% tuning specs
T         = 0.1;     % +/- tuning range as a normalized value
CvarRatio = 3;       % maximum to minimum value of CVar
CswBits   = 3;
CswSegs   = 2^(CswBits);
CvarCswLSBOverlap = 2;

%********************************************************************
% optimization of LC oscillator circuit (with tradeoff curve)
%********************************************************************
% varying phase noise parameter for the tradeoff curve
powers = [];
for PNSpec=0.7e-12:0.2e-12:1e-11
fprintf('  PNSpec = %5.2f dBc/Hz: ', 10*log10(PNSpec) );
cvx_begin gp quiet
% optimization variables
variable D;        % diameter of loop inductor
variable W;        % width of loop inductor
variable SRF;      % self resonance frequency
variable l;        % length of CMOS transistor
variable w;        % width of CMOS transistor
variable I;        % maximum current through CMOS transistor
variable VOsc;     % differential voltage amplitude
variable CT;       % total capacitance of oscillator
variable Csw;      % maximum switching capacitance
variable Cvar;     % minimum variable capacitance
variable IBias;    % bias current
variable CMaxFreq; % capacitor max frequency

% minimize power = Vdd*IBias;
minimize( Vdd*IBias )
subject to
%*******************************************%
% loop inductor definitions and constraints %
%*******************************************%
SRFSpec  = 3*F;
omegaSRF = 2*pi*SRF;

% inductance
L = 2.1e-06*D^(1.28)*(W)^(-0.25)*(F)^(-0.01);
% series resistance
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;
% effective capacitance
C = 1e-11*D+5e-6*D*W;

% area, tank conductance, and inverse quality factor
Area = (D+W)^2;
G    = R/(omega*L)^2;
invQ = R/(omega*L);

% loop constraints
Area <= 0.25e-6;
W <= 30e-6;
5e-6 <= W;
10*W <= D;
D <= 100*W;
SRFSpec <= SRF;
omegaSRF^2*L*C <= 1;

%****************************************%
% transistor definitions and constraints %
%****************************************%
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;

% transistor constraints
2e-6 <= w;
0.13e-6 <= l;
l <= 1e-6;

%***************************************************%
% overall LC oscillator definitions and constraints %
%***************************************************%
invVOsc = (G+GD)/IBias;

% phase noise
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);

% capacitance
Cfix = C+0.5*(CL+Cgs+Cdb+4*Cgd); % fixed capacitance
CDiffMaxFreq = Cfix+0.5*Cvar;

invLoopGain = (G+0.5*GD)/(0.5*GM);

% LC oscillator constraints
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; % loop gain spec
Vbias+Vgs+IBias/2*R/2 <= Vdd;  % bias constraint spec
I == IBias;
cvx_end
fprintf('min_power = %3.2f mW\n', 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)')
PNSpec = -121.55 dBc/Hz: min_power = 19.00 mW
PNSpec = -120.46 dBc/Hz: min_power = 11.41 mW
PNSpec = -119.59 dBc/Hz: min_power = 8.35 mW
PNSpec = -118.86 dBc/Hz: min_power = 6.44 mW
PNSpec = -118.24 dBc/Hz: min_power = 5.64 mW
PNSpec = -117.70 dBc/Hz: min_power = 5.30 mW
PNSpec = -117.21 dBc/Hz: min_power = 5.02 mW
PNSpec = -116.78 dBc/Hz: min_power = 4.77 mW
PNSpec = -116.38 dBc/Hz: min_power = 4.56 mW
PNSpec = -116.02 dBc/Hz: min_power = 4.38 mW
PNSpec = -115.69 dBc/Hz: min_power = 4.21 mW
PNSpec = -115.38 dBc/Hz: min_power = 4.07 mW
PNSpec = -115.09 dBc/Hz: min_power = 3.93 mW
PNSpec = -114.81 dBc/Hz: min_power = 3.81 mW
PNSpec = -114.56 dBc/Hz: min_power = 3.70 mW
PNSpec = -114.32 dBc/Hz: min_power = 3.60 mW
PNSpec = -114.09 dBc/Hz: min_power = 3.51 mW
PNSpec = -113.87 dBc/Hz: min_power = 3.42 mW
PNSpec = -113.67 dBc/Hz: min_power = 3.34 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 = 3.13 mW
PNSpec = -112.92 dBc/Hz: min_power = 3.07 mW
PNSpec = -112.76 dBc/Hz: min_power = 3.01 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 = 2.81 mW
PNSpec = -112.01 dBc/Hz: min_power = 2.77 mW
PNSpec = -111.87 dBc/Hz: min_power = 2.72 mW
PNSpec = -111.74 dBc/Hz: min_power = 2.68 mW
PNSpec = -111.61 dBc/Hz: min_power = 2.64 mW
PNSpec = -111.49 dBc/Hz: min_power = 2.61 mW
PNSpec = -111.37 dBc/Hz: min_power = 2.57 mW
PNSpec = -111.25 dBc/Hz: min_power = 2.54 mW
PNSpec = -111.14 dBc/Hz: min_power = 2.50 mW
PNSpec = -111.02 dBc/Hz: min_power = 2.47 mW
PNSpec = -110.92 dBc/Hz: min_power = 2.44 mW
PNSpec = -110.81 dBc/Hz: min_power = 2.41 mW
PNSpec = -110.71 dBc/Hz: min_power = 2.38 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 = 2.23 mW
PNSpec = -110.04 dBc/Hz: min_power = 2.21 mW 