Distortion in Baseband Pulses

Posted on 2025-06-05 Edited on 2025-11-16 In dsp

Linear distortion includes any amplitude or delay distortion associated with a linear transmission system

Nonlinear distortion includes harmonic distortion, intermodulation distortion (IMD)

amplitude distortion

w0 = 2*pi*1;  % T=1
t = 0:0.01:1.25;

x1 = cos(w0*t);
x2 = -1/3*cos(3*w0*t);
x3 = 1/5*cos(5*w0*t);

subplot(2,1,1)
plot(t, x1, 'm-', LineWidth=1.5); hold on;
plot(t, x2, 'g-', LineWidth=1.5); plot(t, x3, 'b-', LineWidth=1.5);
plot(t, x1+x2+x3, 'r-', LineWidth=3); grid on; xlim([0 1.25])
legend('cos(\omega_0t)', '-1/3cos(3\omega_0t)', '1/5cos(5\omega_0t)', 'cos(\omega_0t)-1/3cos(3\omega_0t)+1/5cos(5\omega_0t)')

subplot(2,1,2)
plot(t, x1+x2+x3, 'r-', LineWidth=2); hold on;
plot(t, x1/2+x2+x3, 'g-', LineWidth=2); 
plot(t, x1+x2+x3/2, 'b-', LineWidth=2); grid on; xlim([0 1.25])
legend('ref', 'Low frequency attenuated', 'high frequency attenuated')

phase delay

Phase delay directly measures the device or system time delay of individual sinusoidal frequency components in the steady-state conditions

group delay

Phase Delay & Group Delay

W. Bae, B. Nikolić and D. -K. Jeong, "Use of Phase Delay Analysis for Evaluating Wideband Circuits: An Alternative to Group Delay Analysis," in IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 25, no. 12, pp. 3543-3547, Dec. 2017, [https://people.eecs.berkeley.edu/~bora/Journals/2017/TVLSI17.pdf]

Phase Response Compensation

Xiaojun Zhou. Think PAM4 Serdes [https://ibis.org/summits/nov17a/zhou.pdf]

fs = 1;
f = (0:0.001:1)*fs;
w = f*2*pi;

H_post = 0.65 - 0.35 * exp(-1j*w*1/fs);
mag_post = abs(H_post);
theta_post = unwrap(angle(H_post));
gd_post = - (theta_post(2:end) - theta_post(1:end-1))./(w(2:end) - w(1:end-1));

H_pre = -0.35 +  0.65 * exp(-1j*w*1/fs);
mag_pre = abs(H_pre);
theta_pre = unwrap(angle(H_pre));
gd_pre = - (theta_pre(2:end) - theta_pre(1:end-1))./(w(2:end) - w(1:end-1));

subplot(3,1,1)
plot(f, mag_post, 'r', LineWidth=2); hold on; plot(f, mag_pre, 'b', LineWidth=2);
grid on; legend('Post Tap FFE', 'Pre Tap FFE'); title('FFE Magnitude Response')

subplot(3,1,2)
plot(f, theta_post, 'r', LineWidth=2); hold on; plot(f, theta_pre, 'b', LineWidth=2);
grid on; legend('Post Tap FFE', 'Pre Tap FFE'); title('FFE Phase Response')

subplot(3,1,3)
plot(f(1:end-1), gd_post, 'r', LineWidth=2); hold on; plot(f(1:end-1), gd_pre, 'b', LineWidth=2);
grid on; legend('Post Tap FFE', 'Pre Tap FFE'); title('FFE Group Delay')

Nonlinearity

Even-Order Distortion

Odd-order distortion: symmetry

Even-Order Distortion: non-symmetry (Effect of Mismatch)

[http://cc.ee.ntu.edu.tw/~ecl/Courses/105AIC/lock/Analog_Chapter_09_Nonlinearity%20and%20Mismatch.pdf]

reference

Hollister, Allen L. Wideband Amplifier Design. Raleigh, NC: SciTech Pub., 2007.

Starič, P. & Margan, E.. (2006). Wideband Amplifiers. 10.1007/978-0-387-28341-8. [pdf]

Haykin, Simon S., and Michael Moher. Communication Systems. 5th ed. John Wiley & Sons, 2009.

—. Digital Communication Systems. 1st edition. Wiley, 2013. [pdf]

Carlson, A. Bruce, and Paul B. Crilly. Communication Systems: An Introduction to Signals and Noise in Electrical Communication. 5th ed. Boston: McGraw-Hill Higher Education, 2010. [pdf]

Pupalaikis, Peter. (2006). Group Delay and its Impact on Serial Data Transmission and Testing. [https://cdn.teledynelecroy.com/files/whitepapers/group_delay-designcon2006.pdf]

Pupalaikis, Peter & Yudin, Eric. (2005). Eye Patterns in Scopes. [https://cdn.teledynelecroy.com/files/whitepapers/eye_patterns_in_scopes-designcon_2005.pdf]

Young W. Lim. Group Delay and Phase Delay (1A) [https://upload.wikimedia.org/wikiversity/en/e/e3/Misc.1.A.GroupPhase.20120719.pdf]

Group delay and phase delay example [https://dspillustrations.com/pages/posts/misc/group-delay-and-phase-delay-example.html]

Arkonaire. What is the difference between phase delay and group delay?[https://dsp.stackexchange.com/a/51532/59253]

Andor Bariska. Time Machine, Anyone? [https://www.dsprelated.com/showarticle/54.php]

Julius Orion Smith III. Introduction to Digital Filters: Phase and Group Delay [https://www.dsprelated.com/freebooks/filters/Phase_Group_Delay.html]

Phase delay vs group delay: Common misconceptions. [https://audiosciencereview.com/forum/index.php?threads/phase-delay-vs-group-delay-common-misconceptions.39591/]

Dan Boschen. Why do we care about "Linear Phase Filters"? [link]

CC Chen. Why Group Delay Optimization? [https://youtu.be/Lv7yO_LkKng]

Group and Phase Delay Measurements with Vector Network Analyzer ZVR [https://cdn.rohde-schwarz.com.cn/pws/dl_downloads/dl_application/application_notes/1ez35/1ez35_1e.pdf]

S. Stegemann, W. Mathis. MOS-AK 2012: Interference and Distortion Analysis for Nonlinear Analog Circuits [https://www.mos-ak.org/dresden_2012/publications/T8_Stegemann_MOS-AK_Desden_12.pdf]

Ali Sheikholeslami. A-SSCC 2024 insight: Noise and Distortion, [https://youtu.be/bvsJgHJ19jI]

B. Razavi, "Design considerations for direct-conversion receivers," in IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 44, no. 6, pp. 428-435, June 1997 [http://www.seas.ucla.edu/brweb/papers/Journals/RTCAS97.pdf]

Two-Tone Intermodulation [https://www.ittc.ku.edu/~jstiles/622/handouts/Two-Tone%20Intermodulation.pdf]

Intermodulation Distortion [https://www.ittc.ku.edu/~jstiles/622/handouts/Intermodulation%20Distortion.pdf]

A. Sheikholeslami, "“Noise and Distortion, Part II” [Circuit Intuitions]," in IEEE Solid-State Circuits Magazine, vol. 16, no. 4, pp. 8-11, Fall 2024

A. Sheikholeslami, "Noise and Distortion, Part III [Circuit Intuitions]," in IEEE Solid-State Circuits Magazine, vol. 17, no. 1, pp. 8-11, winter 2025

Ali Sheikholeslami, University of Toronto, A-SSCC 2024 Circuit Insights:FT1 Noise and Distortion [link]