• Analyzed and extracted the inductance, parasitic resistance and capacitance for a spiral inductor layout in IBM 130nm technology using MATLAB code. • Analyzed the improved Q-prediction accuracy by measuring Q factor as Wo/dW at different resonant frequencies from the inductor self-resonant frequency by numerically adding a capacitor (Cnum ) in parallel to the measured Y11 data of spiral inductor equivalent model using MATLAB codes. • Measurement from new method showed significant Q-value to be useful enough all the way up to the self-resonance frequency at 1-5Ghz when compared to unreasonable results from conventional [-Imag(Y11)/ Re(Y11)] value.

1. THE UNIVERSITY OF TEXAS AT DALLAS
ERIK JONSSON SCHOOL OF ENGINEERING & COMPUTER SCIENCE
EERF 6330 RFIC DESIGN Kenneth O.
SPRING 2016
ACCURATE Q-PREDICTION FOR RFIC SPIRAL INDUCTORS
USING THE 3DB BANDWIDTH:
BY ILANGO JEYASUBRAMANIAN (ixj150230)

2. ANALYSIS OF SPIRAL INDUCTORUSED IN LNA;
INDUCTOR LAYOUT:
DRC_CHECK:

3. All the inductance, parasitic resistance and capacitance calculation is based on the following paper, “DESIGN
OF PLANAR RECTANGULAR MICROELECTRONIC INDUCTORS“,H. M. GREENHOUSE,SENIOR MEMBER,
IEEE.
CALCULATION OF TOTAL INDUCTANCE ( L ) :
MATLAB FUNCTION FOR CALCULATINGSELF-INDUCTANCE:
function l=L(len)
a=10e-4;
b=0.6e-4;
l=0.002*len*(log((2*len)/(a+b))+ 0.2505 + ((a+b)/(3*len)) + (1/4));
MATLAB FUNCTION FOR CALCULATINGMUTUAL-INDUCTANCE FOR SAME FILAMENT LENGTHS:
function m1=Ms(l,d,w)
GMD=exp( log(d) - ( ((1/12)*((w/d)^2)) + ((1/60)*((w/d)^4)) + ((1/168)*((w/d)^6))+ ((1/360)*((w/d)^8)) + ((1/660)*((w/d)^10)) ) );
Q=log((l/GMD) + ((1+(l/GMD)^2)^(1/2))) - ((1+(GMD/l)^2)^(1/2)) + (GMD/l);
m1=2*l*Q;
MATLAB FUNCTION FOR CALCULATINGMUTUAL-INDUCTANCE FOR DIFFERENT FILAMENT LENGTHS:
function m2 = Md(lm,lp,lq,d,w)
if lp~=0 & lq~=0
Mmp=Ms((lm+lp),d,w);
Mmq=Ms((lm+lq),d,w);
Mp =Ms(lp,d,w);
Mq =Ms(lq,d,w);
m2 =((Mmp+Mmq)-(Mp+Mq))/2;
elseif lp==0 & lq~=0
Mmp=Ms((lm+lp),d,w);
Mmq=Ms((lm+lq),d,w);
Mp =0;
Mq =Ms(lq,d,w);
m2 =((Mmp+Mmq)-(Mp+Mq))/2;
elseif lp~=0 & lq==0
Mmp=Ms((lm+lp),d,w);
Mmq=Ms((lm+lq),d,w);
Mp =Ms(lp,d,w);
Mq =0;
m2 =((Mmp+Mmq)-(Mp+Mq))/2;
end
MATLAB FUNCTION FOR CALCULATINGTOTAL-INDUCTANCE:
%FILAMENT LENGTHS
l1 = 300e-4;
l2 = 300e-4;
l3 = 300e-4;

4. l4 = 280e-4;
l5 = 280e-4;
l6 = 260e-4;
l7 = 260e-4;
l8 = 150e-4;
lMQ = 60e-4;
%SELF-INDUCTANCE in uH
Lind=L(l1)+L(l2)+L(l3)+L(l4)+L(l5)+L(l6)+L(l7)+L(l8)+L(lMQ)
M15 =Md(280e-4,20e-4,0,20e-4,10e-4);
M51 =Ms(280e-4,20e-4,10e-4);
M26 =Md(260e-4,20e-4,20e-4,20e-4,10e-4);
M62 =Ms(260e-4,20e-4,10e-4);
M37 =Md(260e-4,20e-4,20e-4,20e-4,10e-4);
M73 =Ms(260e-4,20e-4,10e-4);
M48 =Md(150e-4,20e-4,110e-4,20e-4,10e-4);
M84 =Ms(150e-4,20e-4,10e-4);
M3MQ=Md(15e-4,285e-4,0,170e-4,10e-4);
MMQ3=Ms(15e-4,170e-4,10e-4);
%POSITIVE MUTUAL INDUCTANCE in nH
Mpos=M15+M51+M26+M62+M37+M73+M48+M84+M3MQ+MMQ3
M13=Ms(300e-4,300e-4,10e-4);
M31=Ms(300e-4,300e-4,10e-4);
M17=Md(260e-4,20e-4,20e-4,280e-4,10e-4);
M71=Ms(260e-4,280e-4,10e-4);
M35=Md(280e-4,20e-4,0,280e-4,10e-4);
M53=Ms(280e-4,280e-4,10e-4);
M57=Md(260e-4,0,20e-4,260e-4,10e-4);
M75=Ms(260e-4,260e-4,10e-4);
M24=Md(280e-4,0,20e-4,300e-4,10e-4);
M42=Ms(280e-4,300e-4,10e-4);
M28=Md(150e-4,20e-4,130e-4,280e-4,10e-4);
M82=Ms(150e-4,280e-4,10e-4);
M46=Md(260e-4,20e-4,0,280e-4,10e-4);
M64=Ms(260e-4,280e-4,10e-4);
M68=Md(150e-4,0,110e-4,260e-4,10e-4);
M86=Ms(150e-4,260e-4,10e-4);
M1MQ=Md(15e-4,285e-4,0,130e-4,10e-4);

5. MMQ1=Ms(15e-4,130e-4,10e-4);
M5MQ=Md(15e-4,265e-4,0,110e-4,10e-4);
MMQ5=Ms(15e-4,110e-4,10e-4);
%NEGATIVE MUTUAL INDUCTANCE in nH
Mneg=M13+M31+M17+M71+M53+M35+M57+M75+M24+M42+M28+M82+M64+M46+M68+M86+M1MQ+MMQ1+M5MQ+MM
Q5
Total = (Lind*1e3)+Mpos-Mneg
RESULTS:
Total inductance = 2.4963nH
CALCULATION OF CAPACITANCE (Cp):
Epsilon=8.854e-12;
Wmq=10e-6; %WIDTH OF MQ
Hmq=4.79e-6; %HEIGHT OF MQ
Tmq=0.6e-6; %THICKNESS OF MQ
a=(Wmq-(Tmq/2))/Hmq;
c=(2*Hmq)/Tmq;
b=log(1 + c + sqrt(c*(c+2)));
CMQ=3.9*Epsilon*(a+((2*3.14)/b)) %CAPACITANCE OF MQ
Wmg=10e-6; %WIDTH OF MG
Hmg=6.04e-6; %HEIGHT OF MG
Tmg=0.6e-6; %THICKNESS OF MQ
a=(Wmg-(Tmg/2))/Hmg;
c=(2*Hmg)/Tmg;
b=log(1 + c + sqrt(c*(c+2)));
CMG=3.9*Epsilon*(a+((2*3.14)/b)) %CAPACITANCE OF MG
Cp=((CMG*2130e-6)+(CMQ*60e-6))/2 %CAPACITANCE (Cp)
RESULTS:
CAPACITANCE (Cp) = 0.1247pF
CALCULATION OF RESISTANCE (Rs):
%FILAMENT LENGTHS
l1 = 300e-6;
l2 = 300e-6;
l3 = 300e-6;
l4 = 280e-6;
l5 = 280e-6;
l6 = 260e-6;
l7 = 260e-6;
l8 = 150e-6;

6. lMQ= 60e-6;
W = 10e-6;
del=1/sqrt(3.14*1.26e-6*4e7*4e9) %Delta value for skin effect
RMG=0.0339; %SHEET RESISTANCE OF MG
RMQ=0.0339; %SHEET RESISTANCE OF MQ
%RESISTANCE OF EACH MG FILAMENTS
R1 =((l1-(2*W))*RMG)/(2*del);
R2 =((l2-(4*W))*RMG)/(2*del);
R3 =((l3-(4*W))*RMG)/(2*del);
R4 =((l4-(4*W))*RMG)/(2*del);
R5 =((l5-(4*W))*RMG)/(2*del);
R6 =((l6-(4*W))*RMG)/(2*del);
R7 =((l7-(4*W))*RMG)/(2*del);
R8 =((l8-(2*W))*RMG)/(2*del);
%RESISTANCE OF MQ FILAMENT
R_mq=(lMQ*RMQ)/(del);
%RESISTANCE OF ALL CORNERS
R_corner=7*((W/del)+0.5)*RMG;
%RESISTANCE OF CONTACTS
Rcon=0.25/169;
%TOTAL RESISTANCE
R_tot=R1+R2+R3+R4+R5+R6+R7+R8+R_mq+Rcon+R_corner
RESULTS:
TOTAL RESISTANCE (Rs) = 28.5754 Ohm
CALCULATION OF QUALITYFACTOR:
w=2*3.14*4e9;
L=2.4963e-9;
Rs=28.5754;
Q1=(w*L)./Rs
RESULTS:
Q = 2.1944

7. MATLAB CODE FOR CALCULATING Qconv OF INDUCTOR:
Qconvis the conventional quality factor measurement of an inductor done as
(-Imag(y11)/Real(y11)) of an inductor.
CODE:
f=[0:10e5:10e9];
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs));
Img_y11 =imag(y11);
Real_y11=real(y11);
Qc =-(Img_y11./Real_y11)
plot(f,Qc)
ylabel('Qconv')
xlabel('frquency')

8. MATLAB CODE FOR CALCULATING Qbw :
Qbw defines the quality factor of the inductor by the 3db bandwidth of the
inductor Qbw = w/∆𝑤 based on the paper “Estimation Methods for Quality Factors of Inductors Fabricated in Silicon
Integrated Circuit Process Technologies”, Kenneth O,IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 33,
NO. 8, AUGUST 1998.
We can see the bandwidth and frequency stability factor are defined only at the resonant frequency, measured
data can be used to extract them at the self-resonant frequency of an inductor. Hence, Qconv helps to measure the
Q factor only at the inductors self-resonance.
However Qbw helps to measure Q factor at a resonant frequency different from the inductor self-resonant
frequency by numerically adding a capacitor (Cnum ) in parallel to the measured data, and by computing the
parameters at the resonant frequency of the resulting RLC circuit.
At moderate to high frequencies, the commonly used Q definition [-Im(y11)/ Re(y11)] can significantly
underestimate and can even give unreasonable results. Data obtained using the new methods suggest that quality
factors remain high and integrated inductors remain useful all the way up to their self-resonant frequencies, contrary
to the estimation by Qconv.
FOR 1GHZ:
%Added Cnum =2.23pF in parallel for self-resonance at 1GHZ
f=[0.5:10e5:3e9];
c=223e-14
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));
Cnum=(1./(2*3.14*f*c*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs))+ (1./Cnum);
Img_y11 =imag(y11);
Real_y11=real(y11);
Q =-(Img_y11./Real_y11)
subplot(1,2,1)
plot(f,Q)
ylabel('Qc-1GHZ')
xlabel('frquency')
Qc = abs(1./y11)
subplot(1,2,2)
plot(f,Qc)
ylabel('Magnitude of(1/y11)-1GHZ')
xlabel('frquency')

9. b=powerbw(Qc)
Qbw=(2*3.14*1e9)./b
RESULT:
Qbw at 1GHZ = 1.7667e+13
FOR 2GHZ:
%Added Cnum =1.25pF in parallel for self-resonance at 2GHZ
f=[0.5:10e5:10e9];
c=125e-14
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));
Cnum=(1./(2*3.14*f*c*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs))+ (1./Cnum);
Img_y11 =imag(y11);
Real_y11=real(y11);
Q =-(Img_y11./Real_y11)
subplot(1,2,1)
plot(f,Q)
ylabel('Qc-2GHZ')

10. xlabel('frquency')
Qc = abs(1./y11)
subplot(1,2,2)
plot(f,Qc)
ylabel('Magnitude of(1/y11)-2GHZ')
xlabel('frquency')
b=powerbw(Qc)
Qbw=(2*3.14*2e9)./b
RESULT:
Qbw at 2GHZ = 5.8346e+13
FOR 3GHZ:
%Added Cnum =0.695pF in parallel for self-resonance at 3GHZ
f=[0.5:10e5:3e9];
c=6.95e-13
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));
Cnum=(1./(2*3.14*f*c*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs))+ (1./Cnum);
Img_y11 =imag(y11);
Real_y11=real(y11);

11. Q =-(Img_y11./Real_y11)
subplot(1,2,1)
plot(f,Q)
ylabel('Qc-3GHZ')
xlabel('frquency')
Qc = abs(1./y11)
subplot(1,2,2)
plot(f,Qc)
ylabel('Magnitude of(1/y11)-3GHZ')
xlabel('frquency')
b=powerbw(Qc)
Qbw=(2*3.14*3e9)./b
RESULT:
Qbw at 3GHZ = 9.0707e+13
FOR 4GHZ:
%Added Cnum =0.401pF in parallel for self-resonance at 4GHZ
f=[0.5:10e5:3e9];
c=4.01e-13
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));

12. Cnum=(1./(2*3.14*f*c*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs))+ (1./Cnum);
Img_y11 =imag(y11);
Real_y11=real(y11);
Q =-(Img_y11./Real_y11)
subplot(1,2,1)
plot(f,Q)
ylabel('Qc-4GHZ')
xlabel('frequency')
Qc = abs(1./y11)
subplot(1,2,2)
plot(f,Qc)
ylabel('Magnitude of(1/y11)-4GHZ')
xlabel('frequency')
b=powerbw(Qc)
Qbw=(2*3.14*4e9)./b
RESULT:
Qbw at 4GHZ = 1.1696e+14
FOR 5GHZ:
%Added Cnum =0.233pF for self-resonance at 5GHZ

13. f=[0.5:10e5:3e9];
c=2.33e-13
cp =1.2470e-13;
l =2.4963e-9;
Rs =28.5754;
Rsub=10;
Cp1 =(1./(2*3.14*f*cp*i));
Cnum=(1./(2*3.14*f*c*i));
L =(2*3.14*f*l*i);
y11 =(1./(Cp1+Rsub))+(1./(L+Rs))+ (1./Cnum);
Img_y11 =imag(y11);
Real_y11=real(y11);
Q =-(Img_y11./Real_y11)
subplot(1,2,1)
plot(f,Q)
ylabel('Qc-5GHZ')
xlabel('frequency')
Qc = abs(1./y11)
subplot(1,2,2)
plot(f,Qc)
ylabel('Magnitude of(1/y11)-5GHZ')
xlabel('frequency')
b=powerbw(Qc)
Qbw=(2*3.14*5e9)./b
RESULT:
Qbw at 5GHZ = 1.3339e+14