slides 12,13,14,15 have ctle and shunt peaking matlab codes and results

1. Group delay
Matlab vs cadence

2. theory
• Nice reference
• https://en.wikipedia.org/wiki/Group_delay_and_phase_delay
• Phase delay

3. Hand analysis for single pole (RC) case
Group delay phase delay
• Youtube link for following equations
• https://www.youtube.com/watch?v=m9tASJ9DaTY

4. One pole case
• Pole – 5e9
• Default cadence function is not giving expected results
• Written my own measurements
• Verfied the measurements vs hand analysis results from equation in above slide
• The same circuit as below is used for one pole and one zero case
• Inductor is made ‘0” for one pole case
procedure
Hand analysis

5. Comparing group delay between hand
analysis and cadence measurements

6. Matlab one pole case
• f_z1=[10^80]; % zero at infinite location
• f_p1=5e9;
• new=[];
• for i=1 % only one zero pole combination
• k=f_p1/f_z1(i);
• t_freq=logspace(1,11,100000);
• w_l=2*pi*t_freq;
• [b,a] = zp2tf(f_z1(i),f_p1,k);
• h=freqs(b,a,w_l);
• mag=20*log10(abs(h));
• subplot(2,1,1)
• semilogx(w_l,mag);
• hold on;
• phase = angle(h);
• pdiff =diff(phase);
• w_l_new=diff(w_l);
• grpdel = (pdiff./w_l_new)/(2*pi); % adding 2*pi since 2*pi get cancelled
between pdiff and w_l_new
• grpdel_max=max(grpdel);
• grpdel_min=min(grpdel);
• grpdel_pp=grpdel_max-grpdel_min
• new(i,1)=grpdel_pp;
• subplot(2,1,2)
• semilogx(w_l(1:end-1),grpdel)
• xlabel('Frequency (rad/s)')
• ylabel('Group delay (s)')
• end
• hold off
1. No matlab codes readily available for group delay
2. Default matlab codes (grpdelay) are for digital filters
1. https://www.mathworks.com/help/signal/ref/grpdelay.html
• Grpdelay function doesn’t give accurate results
• Waveform shapes from my code are same as that of spectre and also
handanalysis
• Got confused so much since both groupDelay (spectre) and grpdelay
(matlab) are inaccurate
• Finally settled with my methods by comparing with handanalysis

7. Matlab one pole case - results

8. One pole and one zero case
• Pole – 5e9
• Zero – 2e9, 3e9,4e9,5e9,6e9,7e9
• Circuit to produce a zero (R and L) and a pole (R and C)
• Dc gain = 1 (R1.gm.R1)
• Gm=R1*R1

9. spectre results
• As zero location is moved, dc gain is 0 but peak ac gain is decreasing
• Group delay peak to peak (gdpp) is highest when zero is at 2G
• 3G vs 7G – delta is 2G but gdpp is different

10. Matlab code
• f_z1=[2e9,3e9,4e9,5e9,6e9,7e9];
• f_p1=5e9;
• new=[];
• clf;
• for i=1:1:6
• k=f_p1/f_z1(i);
• t_freq=logspace(1,11,100000);
• w_l=2*pi*t_freq;
• [b,a] = zp2tf(f_z1(i),f_p1,k);
• h=freqs(b,a,w_l);
• mag=20*log10(abs(h));
• subplot(2,1,1)
• semilogx(w_l,mag);
• hold on;
• phase = angle(h);
•
• pdiff =diff(phase);
• w_l_new=diff(w_l);
• grpdel = (pdiff./w_l_new)./(2*pi);
• grpdel_max=max(grpdel);
• grpdel_min=min(grpdel);
• grpdel_pp=grpdel_max-grpdel_min;
• new(i,1)=grpdel_pp;
• subplot(2,1,2)
• semilogx(w_l(1:end-1),grpdel)
• xlabel('Frequency (rad/s)')
• ylabel('Group delay (s)')
• hold on;
• end
• hold off
• fprintf("%3.2e %s",new(1));
• fprintf("%3.2e %s",new(2));
• fprintf("%3.2e %s",new(3));
• fprintf("%3.2e %s",new(4));
• fprintf("%3.2e %s",new(5));
• fprintf("%3.2e %s",new(6));

11. Matlab results
• Frequency response matches with spectre results
• Peak gain when zero @ 2GHz – 7.94dB and 7Ghz - -2.9dB
• Matlab and spectre agree with each other

12. 2 stage ctle, 2 zeroes, 4 poles
• f_z1=2.5e9;
• f_z2=2.75e9;
• f_p1=6e9;
• f_p2=7e9;
• f_p3=7e9;
• f_p4=8e9;
• f_p5=9e9;
• clf;
•
• k=(f_p1*f_p2*f_p3*f_p4*f_p5)/(f_z1*f_z2);
• f_p=[f_p1,f_p2,f_p3,f_p4,f_p5];
• f_z=[f_z1,f_z2]';
• t_freq=logspace(1,11,100000);
• w_l=2*pi*t_freq;
• [b,a] = zp2tf(f_z,f_p,k);
• h1=freqs(b,a,t_freq);
• hoverall=h1.*h1;
• mag1=20*log10(abs(h1));
• magoverall=20*log10(abs(hoverall));
• peaking=max(mag);
• new(i,1)=peaking;
• subplot(2,1,1)
• semilogx(t_freq,mag1);
• hold on
• subplot(2,1,2)
• semilogx(t_freq,magoverall);
• hold on;
• fprintf("%3.2f %s",new(1));
• Intention is to replicate fx3g2 ctle at 0 dc gain and peaking of 12dB
• See that the bw is degrading with 2 stages even though peak gain is increasing
• Get a rough idea of where poles & zeroes are
• 3 poles are obvious in the first stage, added 4,5 to model 3rd stage

13. Shunt peaking

14. Matlab code
• R=100;
• L=[0:1:10].*(10^-9);
• C=600e-15;
• clf;
• for i=1:1:length(L)
• num = [L(i) R];
• den=[L(i)*C R*C 1];
• H = tf(num,den);
• figure(1);
• hold on;
• bode(H)
• Bd = bode(H);
• dbdrop = -3;
• fb(i) = bandwidth(H,dbdrop);
• max_gain = max(abs(20*log10(bode(H))));
• size_Bd=size(Bd);
• dc_gain_array=reshape(Bd,[1,size_Bd(3)]);
• dc_gain=20*log10(dc_gain_array(1));
• peaking(i)=max_gain-dc_gain;
• end
• for i=1:1:length(L)
• fprintf("(%3.2f %3.4e) %s", peaking(i),fb(i))
• end
• hold off
• Inductor is swept from 0H to 5nH
• Peaking and bandwidth increase with inductance value and reaches 1.5dB, then peaking continues to increase
while band width decreases
• (0.00 1.6627e+10) (0.00 2.0567e+10) (0.00 2.6522e+10) (0.24 2.9946e+10) (1.24 3.0747e+10) (2.30
3.0638e+10) (3.30 3.0263e+10) (4.21 2.9829e+10) (5.04 2.9404e+10) (5.79 2.9012e+10) (6.48 2.8657e+10) >>

15. Bw decreases