Receiver Front Ends

image-20260924012204914

source-degeneration -> +resonator-based CTLE for higher peaking frequency

image-20260925091849782

input network

image-20250706110415914


image-20250611075951974

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>> 10e6/2/pi/400/50

ans =

79.5775

CTLE design target

peaking gain + curve shape

CTLE transfer function

Circuit Insights @ ISSCC2025: Circuits for Wireline Communications - Kevin Zheng [https://youtu.be/8NZl81Dj45M&t=1045]

image-20260328182328792

image-20260328182339762


Why Shunt-peaking or Source Degenerated type Active CTLE? [https://youtu.be/EFMZG-FIWeo]

image-20260519232914332

Shunt Peaking broaden the RC bandwidth

image-20260519233200484

image-20260526210821835

image-20260526210739466

curve shape

PCIe Gen6 Channel and Reference Package S4P Models for Rx Stressed Eye Calibration

image-20251204005909804

Above curve demonstrate that only zero is not enough to compensate channel+pkg loss (>20 dB/decade), peaking or Complex-Conjugate Poles is necessary

image-20251204005738743


S. Shahramian et al., "30.5 A 1.41pJ/b 56Gb/s PAM-4 Wireline Receiver Employing Enhanced Pattern Utilization CDR and Genetic Adaptation Algorithms in 7nm CMOS," 2019 IEEE International Solid-State Circuits Conference - (ISSCC), San Francisco, CA, USA, 2019 [pdf]

image-20251203231733124


P. A. Francese et al., "10.6 continuous-time linear equalization with programmable active-peaking transistor arrays in a 14nm FinFET 2mW/Gb/s 16Gb/s 2-Tap speculative DFE receiver," 2015 IEEE International Solid-State Circuits Conference - (ISSCC) Digest of Technical Papers, San Francisco, CA, USA, 2015 [https://sci-hub.se/10.1109/ISSCC.2015.7062988]

image-20251203232523501


Z. Li, M. Tang, T. Fan and Q. Pan, "A 56-Gb/s PAM4 Receiver Analog Front-End With Fixed Peaking Frequency and Bandwidth in 40-nm CMOS," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 9, pp. 3058-3062, Sept. 2021 [slides] [paper]

In the active copper cable (ACC) application, it is necessary to give different equalizations at the same frequency according to different cable lengths, Therefore, the AFE with fixed peaking frequency and constant bandwidth is desirable for these applications

image-20251217224711701

Low-Frequency CTLE (LF-CTLE)

S. Parikh et al., "A 32Gb/s wireline receiver with a low-frequency equalizer, CTLE and 2-tap DFE in 28nm CMOS," 2013 IEEE International Solid-State Circuits Conference Digest of Technical Papers, San Francisco, CA, USA, 2013 [https://sci-hub.se/10.1109/ISSCC.2013.6487622]

T. Shibasaki et al., "A 56-Gb/s receiver front-end with a CTLE and 1-tap DFE in 20-nm CMOS," 2014 Symposium on VLSI Circuits Digest of Technical Papers, Honolulu, HI, USA, 2014, pp. 1-2

Yasuo Hidaka Comment #146, #174: Low-Frequency CTLE to support 3m cable w/o FEC [https://www.ieee802.org/3/by/public/Sept15/hidaka_3by_01_0915.pdf]

image-20251217233444843

image-20251217234434659

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Equalization Noise Enhancement

Advanced Signal Integrity for High-Speed Digital Designs, S. H. Hall and H. L. Heck, John Wiley & Sons, 2009

CC Chen, Why CTLE? [https://youtu.be/zsuJMqadaKY]

image-20251021211402274

image-20250904235434247

Assuming \(\mathrm{SNR}(f) = \frac{S_x(f)}{S_n(f)}\)


trade-offs between noise amplification and signal equalization

Gm-TIA

H. Kimura et al., "A 28 Gb/s 560 mW Multi-Standard SerDes With Single-Stage Analog Front-End and 14-Tap Decision Feedback Equalizer in 28 nm CMOS," in IEEE Journal of Solid-State Circuits, vol. 49, no. 12, pp. 3091-3103, Dec. 2014 [https://ieeexplore.ieee.org/ielx7/4/6963535/06894632.pdf]

Pisati, et.al., "Sub-250mW 1-to-56Gb/s Continuous-Range PAM-4 42.5dB IL ADC/DAC- Based Transceiver in 7nm FinFET," 2019 IEEE International Solid-State Circuits Conference (ISSCC), 2019 [https://sci-hub.se/10.1109/ISSCC.2019.8662428]

Z. Li, M. Tang, T. Fan and Q. Pan, "A 56-Gb/s PAM4 Receiver Analog Front-End With Fixed Peaking Frequency and Bandwidth in 40-nm CMOS," in IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 68, no. 9, pp. 3058-3062, Sept. 2021 [slides] [paper]

K. Kwon et al., "A 212.5Gb/s Pam-4 Receiver With Mutual Inductive Coupled Gm-Tia in 4nm Finfet," 2025 Symposium on VLSI Technology and Circuits (VLSI Technology and Circuits), Kyoto, Japan, 2025

Bae, W. (2019). CMOS Inverter as Analog Circuit: An Overview. Journal of Low Power Electronics and Applications. [pdf]

CTLE, with Gm + TIA structure

image-20260921214634581

image-20250904202636824


Chongyun ZHANG, 2025, "Energy-Efficient CMOS Optical Receiver for Short-Reach Data Center Application,". [slides, paper]

image-20251202222813043

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Cherry-Hooper Amplifier

image-20260921235713422

image-20260921235635071

Resonator-Based CTLE

image-20260925162456941

Passive series peaking

D. Pfaff et al., "7.3 A 224Gb/s 3pJ/b 40dB Insertion Loss Transceiver in 3nm FinFET CMOS," 2024 IEEE International Solid-State Circuits Conference (ISSCC), San Francisco, CA, USA, 2024, pp. 128-130, doi: 10.1109/ISSCC49657.2024.10454537.

image-20260922003739424

At DC \[ i_f = g_{md1}v_f \quad i_f = (v_f - v_o)/R_f \qquad \Longrightarrow \qquad \frac{v_o}{v_i} = -\frac{g_{m1}}{g_{md1}} + g_{m1}R_f \] since \(R_f=0\) \[ A_{DC} = -\frac{g_{m1}}{g_{md1}} \]

passive_series_peaking.drawio

\[ \frac{V_o}{V_i}(s) = -g_{m1}R_s\cdot \frac{\frac{1}{LC}}{s^2 + \frac{R_s+R_{LS}}{L}s + \frac{1}{LC}}=-g_{m1}R_s\cdot \frac{\omega_n^2}{s^2+\frac{\omega_n}{Q}s+\omega_n^2} \]

where \[ \boxed{Q=\frac{\omega_n L}{R_s + R_{LS}} \qquad \qquad \omega_n = \frac{1}{\sqrt{LC}}} \]

The \(Q\) is the resonator loaded quality factor

That is \[ A_{DC}=-g_{m1}R_s\qquad\qquad A_{HF}=jg_{m1}R_s\cdot Q \qquad\qquad \frac{A_{HF}}{A_{DC}} = Q \]

where \(A_{HF}\) is the gain at resonance


image-20260922003625379

image-20260922002932197

image-20260922003026369

Q-Shaping (LC-tuned Amplifier)

Y. Krupnik et al., "112 Gb/s PAM4 ADC Based SERDES Receiver for Long-Reach Channels in 10nm Process," 2019 Symposium on VLSI Circuits, Kyoto, Japan, 2019, pp. C266-C267, [https://sci-hub.jp/10.23919/VLSIC.2019.8778136]

—, "112-Gb/s PAM4 ADC-Based SERDES Receiver With Resonant AFE for Long-Reach Channels," in IEEE Journal of Solid-State Circuits, vol. 55, no. 4, pp. 1077-1085, April 2020, [https://sci-hub.jp/10.1109/JSSC.2019.2959511]

S. Kiran et al., "A 56GHz Receiver Analog Front End for 224Gb/s PAM-4 SerDes in 10nm CMOS," 2021 Symposium on VLSI Circuits, Kyoto, Japan, 2021, pp. 1-2, [https://sci-hub.jp/10.23919/VLSICircuits52068.2021.9492471]

Y. Segal et al., "A 1.41pJ/b 224Gb/s PAM-4 SerDes Receiver with 31dB Loss Compensation," 2022 IEEE International Solid-State Circuits Conference (ISSCC), San Francisco, CA, USA, 2022, pp. 114-116, [https://sci-hub.jp/10.1109/ISSCC42614.2022.9731794]

A. Khairi et al., "A 1.41-pJ/b 224-Gb/s PAM4 6-bit ADC-Based SerDes Receiver With Hybrid AFE Capable of Supporting Long Reach Channels," in IEEE Journal of Solid-State Circuits, vol. 58, no. 1, pp. 8-18, Jan. 2023, doi: 10.1109/JSSC.2022.3211475

D. Pfaff et al., "A 224 Gb/s 3 pJ/bit 40 dB Insertion Loss Transceiver in 3-nm FinFET CMOS," in IEEE Journal of Solid-State Circuits, vol. 60, no. 1, pp. 9-22, Jan. 2025, doi: 10.1109/JSSC.2024.3466092

image-20260924003949332

image-20260923233823241

image-20260924002757637

image-20260924011450698


image-20260921234359120

At resonant frequency \[ \boxed{|A_v|= \frac{g_m} {1+\left(\dfrac{g_mR_D}{1+j\omega R_DC_D}\right)} Q_{\mathrm{ind}}\omega L, \qquad \omega=\frac{1}{2\pi\sqrt{L_C L_L}}} \] where \(Q_{\mathrm{ind}}=\frac{\omega L}{R_L}, \qquad R_p=Q_{\mathrm{ind}}^{\,2}R_L=Q_{\mathrm{ind}}\omega L\)

Q-Shaping w/ Parallel RLC

H. Park et al., "7.4 A 112Gb/s DSP-Based PAM-4 Receiver with an LC-Resonator-Based CTLE for >52dB Loss Compensation in 4nm FinFET," 2025 IEEE International Solid-State Circuits Conference (ISSCC), San Francisco, CA, USA, 2025, pp. 142-144, doi: 10.1109/ISSCC49661.2025.10904638.

image-20260925162753669

With Zero-Forcing, inverse of \(h_0 \sim h_1\) only

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┌ 1    0    0    0 ┐ ┌c0┐   ┌1┐
│ 0.7 1 0 0 │ │c1│ = │0│
│ 0 0.7 1 0 │ │c2│ │0│
└ 0 0 0.7 1 ┘ └c3┘ └0┘
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% Define the coefficient matrix A
A = [1 0 0 0;
0.7 1 0 0;
0 0.7 1 0;
0 0 0.7 1];

% Define the right-hand side vector b
b = [1;
0;
0;
0];

% Solve the linear system A * c = b for c
% The backslash operator (\) is the recommended way to solve linear systems in MATLAB
c = A \ b;

% Display the result
disp('Vector c:');
disp(c');

% Vector c:
% 1.0000 -0.7000 0.4900 -0.3430

the other method: Treat \(z^{-1}\) as an ordinary variable and divide 1 by \(1+0.7z^{-1}\), working in ascending powers of \(z^{-1}\)

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                 1  − 0.7z⁻¹ + 0.49z⁻² − 0.343z⁻³ + …      ← quotient = c
┌─────────────────────────────────────────
1 + 0.7z⁻¹ │ 1
│ 1 + 0.7z⁻¹ ← 1 × divisor
│ ───────────
│ − 0.7z⁻¹ ← remainder
│ − 0.7z⁻¹ − 0.49z⁻² ← (−0.7z⁻¹) × divisor
│ ──────────────────
│ + 0.49z⁻²
│ + 0.49z⁻² + 0.343z⁻³ ← (0.49z⁻²) × divisor
│ ───────────────────
│ − 0.343z⁻³
│ …

Use \(1/(1 − r) = 1 + r + r^2 + \dots\) and \(r=-\alpha z^{-1}\) \[ \boxed{\frac{1}{1+\alpha z^{-1}} = 1 - \alpha z^{-1} + \alpha \left( \alpha z^{-2} - \alpha^2 z^{-3} + \dots \right)} \] that is \[ \frac{1}{1+0.7z^{-1}} = 1 - 0.7z^{-1} + 0.7\left( 0.7 z^{-2} - 0.49 z^{-3} + \dots \right) \]

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% Define the coefficient matrix A
A = [1 0 0 0 0 0;
0.7 1 0 0 0 0;
0.48 0.7 1 0 0 0;
0.35 0.48 0.7 1 0 0;
0.27 0.35 0.48 0.7 1 0;
0.22 0.27 0.35 0.48 0.7 1];

% Define the right-hand side vector b
b = [1;
0;
0;
0;
0;
0];


% Solve the linear system A * c = b for c
% The backslash operator (\) is the recommended way to solve linear systems in MATLAB
c = A \ b;

% Display the result
disp('Vector c:');
disp(c');

% Vector c:
% 1.0000 -0.7000 0.0100 -0.0210 -0.0151 -0.0138

“Inverse of 36 dB LR Channel Response” shows the impulse-response taps of the inverse filter/equalizer.

CTLE1: \(1-\alpha z^{-1}\), without pole

CTLE2: \(1-\alpha z^{-1} + c_1 (\beta z^{-2} - \beta^2 z^{-3} + \dots) = 1 - \alpha z^{-1} + \frac{c_1\beta z^{-2}}{1 + \beta z^{-1}}\), with pole \(-\beta\)

image-20260925180121841

image-20260925184115093

image-20260925184603380

image-20260925184646942

The Summer response is also treated as an impulse-response tap sequence

when the starting sequence is the channel’s pulse response, convolving it with the equalizer’s impulse-response taps gives the equalized pulse-response taps:

\[ p_{\text{out}}[n]=p_{\text{channel}}[n]*h_{\text{EQ}}[n] \]

The distinction is whether the transmitted pulse is already included:

\[ \underbrace{p_{\text{TX}}*h_{\text{channel}}}_{p_{\text{channel}}} *h_{\text{EQ}} =p_{\text{out}} \]

So:

  • Pulse response ∗ impulse response → pulse response.
  • Impulse response ∗ impulse response → combined impulse response.

If CTLE_HF and Summer are both represented by their block impulse responses, their convolution gives the combined impulse response. Including the transmitted pulse gives the pulse response.

shunt peaking

image-20260608215130203

image-20251206000303668

\(\color{red}m=\frac{R^2C}{L}\) is the ratio of the \(R/L\) zero frequency to the original RC pole frequency \(1/RC\), and therefore measures how aggressively the zero compensates the intrinsic RC roll-off.

[Gist link]

image-20260526211605905

image-20260526211624229

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# Normalize R = C = 1
R = 1.0
C = 1.0

# Frequency sweep
w = np.logspace(-2, 2, 20000)

# Shunt peaking transfer function
#
# R + sL
# H(s) = ---------
# 1 + sRC + s^2 LC
#
# normalized low-frequency gain = 1
#
def H(jw, L):
s = 1j * jw
return (R + s*L) / (R + s*R*R*C + s*s*L*R*C)

# Sweep inductance
Lvals = np.linspace(0.001, 1.5, 300)

image-20260608220405307

image-20260608220440363

[Gist link]

image-20260608224954010

image-20260921235234693


image-20260611225858681

image-20260611225951811

[Gist link]

shunt_chatgpt

image-20260611233156089

series peaking

image-20260526230433602

image-20260526230805917

T-Coil Peaking

Jri Lee. ISSCC 2009 Tutorial. CMOS Circuit Techniques for High Speed Wireline Transceivers [http://cc.ee.ntu.edu.tw/~jrilee/course/2009_Tutorial_10.pdf]

CC Chen. Why SerDes Needs a Rule of Thumb for T-Coil Design? [https://youtu.be/RIQLYQG2u0A]

Capacitor Splitting + Magnetic Coupling of a transformer

image-20251022234854155

image-20251022235133839

tcoil-tran.drawio


alternative analysis with the below 3 uncoupled inductors model

tcoil-tran-3L.drawio


Three uncoupled inductors model

image-20251126173130097

tcoil-Y.drawio \[\begin{align} V_{P13} &= I_1\cdot sL_1 + I_2\cdot sM = I_1\cdot s(L_1+M) + (I_1-I_2)\cdot s(-M) \\ V_{P23} &= -I_2\cdot sL_2 - I_1\cdot sM = -I_2\cdot s(L_2 + M) + (I_1-I_2)\cdot s(-M) \end{align}\]

The negative inductor \(-M\) can be seen as capacitor \[ -j\omega M = \frac{1}{j}\omega M = \frac{1}{j\omega \frac{1}{\omega^2 M}} \] That is \(C_{-M} = \frac{1}{\omega^2 M} \approx 10 \times C_E\)


image-20260715221444331

T-coil w/ inverted mutual coupling

J. Kim, J. -K. Kim, B. -J. Lee and D. -K. Jeong, "Design Optimization of On-Chip Inductive Peaking Structures for 0.13- μm CMOS 40-Gb/s Transmitter Circuits," in IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 56, no. 12, pp. 2544-2555, Dec. 2009 [https://sci-hub.st/10.1109/TCSI.2009.2023772]

TODO 📅

Triple Resonance

TODO 📅

image-20251206000718234


series resonance \(\omega_\text{res}\)

Assuming, \(I_\text{in}=\cos\omega_r t\) and \(V_\text{out}=g\cos(\omega_r t +\theta)\)

with \(I_\text{in} = C_L\frac{\mathrm{d}V_\text{out}}{\mathrm{d}t}\), yield \(g=\sqrt{\frac{L}{C}}\) and \(\theta=- \frac{\pi}{2}\), i.e. \(V_\text{out} = \sqrt{\frac{L}{C}}\cos(\omega_r t - \frac{\pi}{2})\)

Active Inductor

B. Razavi, "The Active Inductor [A Circuit for All Seasons]," in IEEE Solid-State Circuits Magazine, vol. 12, no. 2, pp. 7-11, Spring 2020 [https://www.seas.ucla.edu/brweb/papers/Journals/BR_SSCM_2_2020.pdf]

activeInd

\[\begin{align} A &= \frac{g_mR_L}{1+(g_{\text{m}_{\text{dio}}}+ g_{\text{ds}_\text{tot}})R_L}\cdot \frac{1+R_pC_Ps}{1+\frac{(1+g_{\text{ds}_{\text{tot}}}R_L)R_PC_P+C_PR_L+R_LC_L}{1+(g_{\text{m}_{\text{dio}}}+g_{\text{ds}_\text{tot}})R_L}s + \frac{R_LC_LR_PC_P}{1+(g_{\text{m}_\text{dio}}+g_{\text{ds}_{\text{tot}}})R_L}s^2} \\ &= \frac{g_mR_L}{1+(g_{\text{m}_{\text{dio}}}+ g_{\text{ds}_{\text{tot}}})R_L}\cdot \frac{R_PC_P}{ \frac{R_LC_LR_PC_P}{1+(g_{\text{m}_{\text{dio}}}+g_{\text{ds}_{\text{tot}}})R_L}}\cdot \frac{1/(R_PC_P)+s}{s^2 + \frac{(1+g_{\text{ds}_{\text{tot}}}R_L)R_PC_P+C_PR_L+R_LC_L}{R_PC_P}s + \frac{1+(g_{\text{m}_{\text{dio}}}+g_{\text{ds}_\text{tot}})R_L}{R_LC_LR_PC_P}} \\ &= A_0 \cdot A(s) \end{align}\]

That is

\[\begin{align} \omega_z &= \frac{1}{R_PC_P} \tag{1} \\ \omega_n &= \sqrt{\frac{1+(g_{\text{m}_{\text{dio}}}+ g_{\text{ds}_\text{tot}})R_L}{R_LC_LR_PC_P}} = \sqrt{\omega_{p0}\omega_z} \\ \zeta & = \frac{(1+g_{\text{ds}_\text{tot}}R_L)R_PC_P+C_PR_L+R_LC_L}{R_PC_P} \frac{1}{2 \omega_n} \end{align}\]

Where \[\begin{align} \omega_{p0} &= \frac{1}{(R_L||\frac{1}{g_{\text{m}_{\text{dio}}}}||\frac{1}{g_{\text{m}_{\text{tot}}}})C_L} \tag{2} \end{align}\]

Here, relate \(\omega_{p0}\) and \(\omega_z\) by coefficient \(\alpha\) \[ \omega_{p0} = \alpha \cdot \omega_z \tag{3} \] This way \[ \omega_n= \sqrt{\alpha}\cdot \omega_z \]

\[ \zeta = \frac{1}{2}(K\sqrt{\alpha}+\frac{1+C_P/C_L}{\sqrt{\alpha}}) \tag{4} \]

where \[ K = \frac{R_L||\frac{1}{g_{\text{m}_{\text{dio}}}}||\frac{1}{g_{\text{m}_{\text{tot}}}}}{R_L||g_\text{ds\_tot}} \]

And \(A(s)\) can be expressed as \[ A(s) = \frac{\frac{s}{\omega_z}+1}{\frac{s^2}{\omega_n^2}+2\frac{\zeta}{\omega_n}s+1} \] It magnitude in dB \[ A_\text{dB} = 10\log\frac{1+(\omega/\omega_z)^2}{1+(\omega/\omega_n)^4+2\omega^2(2\zeta^2-1)/\omega_n^2} \] Substitute \(\omega_n\) with Eq (2), followed is obtained \[ A_\text{dB} = 10\log{\frac{\alpha^2(\omega_z^4 + \omega_z^2\omega^2)}{\alpha^2\omega_z^4+\omega^4+2\alpha\omega_z^2(2\zeta^2-1)\omega^2}} \] peaking frequency \[ \omega_\text{peak} = \omega_z\cdot \sqrt{\sqrt{(\alpha+1)^2 - 4\alpha \zeta^2}-1} \] If \(\zeta=1\) \[ \omega_{A_\text{dB = 0dB} } = \sqrt{1-2/\alpha}\cdot \omega_{p0} \qquad \omega_\text{peak} = \omega_z\sqrt{\alpha-2} \qquad A_\text{dB,peak} = 10\log\frac{\alpha^2}{4(\alpha-1)} \]

Negative Capacitance Circuit

Negative Miller Capacitance

S. Gondi and B. Razavi, "Equalization and Clock and Data Recovery Techniques for 10-Gb/s CMOS Serial-Link Receivers," in IEEE Journal of Solid-State Circuits, vol. 42, no. 9, pp. 1999-2011 [pdf]

Sam Palermo. ECEN620 Lecture 14: Limiting Amplifiers (LAs) [https://people.engr.tamu.edu/spalermo/ecen620/lecture14_ee620_limiting_amps.pdf]

image-20251028221403199

image-20251028232644575 \[ C_{d1} = C_{dd1} + (1+\frac{1}{|A_{gd}|})C_{gd1} \] where \(A_{gd}\lt 0\)

image-20251028232707189

For differential mode input, effective input capacitance \[ C_{in} = C_{gs} +(1+A_{dm}) C_{gd}+\color{red}(1-A_{dm})C_n \] and effective output capacitance \[ C_{out} = C_{dd} + (1+\frac{1}{A_{dm}})C_{gd}+\color{red} (1-\frac{1}{A_{dm}})C_n \] That is \(C_n\) deteriorate the effective output capacitance

For common mode input, effective input capacitance \[ C_{in} = C_{gs} + (1+A_{cm}) C_{gd}+ \color{red}(1+A_{cm})C_n \] and effective output capacitance \[ C_{d1} = C_{dd} + (1+\frac{1}{A_{cm}})C_{gd}+\color{red} (1+\frac{1}{A_{cm}})C_n \] i.e., \(C_n\) deteriorate both effective input capacitance and effective output capacitance, unfortunately


effective input capacitance \(\Pi\) model, which is appropriate for both differential input and common mode input

nmc_pi_in.drawio

Suppose \(C_n=C_{gd}\), effective differential input capacitance is same with effective common-mode input capacitance (\(C_n=\frac{A_{dm}-A_{cm}}{A_{dm}+A_{cm}}C_{gd}\))



XCP with Capacitor

B. Razavi, "The Cross-Coupled Pair - Part III [A Circuit for All Seasons]," IEEE Solid-State Circuits Magazine, Issue. 1, pp. 10-13, Winter 2015. [https://www.seas.ucla.edu/brweb/papers/Journals/BR_Magzine3.pdf]

S. Galal and B. Razavi, "10-Gb/s Limiting Amplifier and Laser/Modulator Driver in 0.18um CMOS Technology,” IEEE Journal of Solid-State Circuits, vol. 38, pp. 2138-2146, Dec. 2003.[https://www.seas.ucla.edu/brweb/papers/Journals/G&RDec03_2.pdf]

A. Sheikholeslami, "Bandwidth Extension [Circuit Intuitions]," in IEEE Solid-State Circuits Magazine, vol. 7, no. 2, pp. 8-11, Spring 2015 [https://www.eecg.utoronto.ca/~ali/papers/mag-spr-15-bandwidth-extention.pdf]

The Cross-Coupled Pair (XCP) can operate as an impedance negator [a.k.a. a negative impedance converter (NIC)]

A common application is to create a negative capacitance that can cancel the positive capacitance seen at a port, thereby improving the speed

image-20240922174319496 \[ I_{NIC} =\frac{V_{im} - V_{ip}}{\frac{2}{g_m}+\frac{1}{sC_c}} = \frac{-2V_{ip}}{\frac{2}{g_m}+\frac{1}{sC_c}} \] Therefore \[ Z_{NIC} = \frac{V_{ip} - V_{im}}{I_{NIC}}=\frac{2V_{ip}}{I_{NIC}} =- \frac{2}{g_m}-\frac{1}{sC_c} \] half-circuit

If \(C_{gd}\) is considered, and apply miller effect. half equivalent circuit is shown as below

nic.drawio


image-20251204223338959

dual-diode based ESD protection

image-20260801014821774

??? which diodes are used in right topology — both pdiode and ndiode are used


image-20260801022107783

reference

T. Chan Carusone, T. O. Dickson, S. Palermo, S. Shekhar and M. Mansuri, "Modern Wireline Transceivers," in IEEE Journal of Solid-State Circuits, vol. 61, no. 2, pp. 395-422, Feb. 2026 [https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=11311714]

Miguel Gandara. CICC2025 Circuits Insights: Wireline Receiver Circuits [https://youtu.be/X4JTuh2Gdzg]

Elad Alon, ISSCC 2014, "T6: Analog Front-End Design for Gb/s Wireline Receivers"

Byungsub Kim, ISSCC 2022, "T11: Basics of Equalization Techniques: Channels, Equalization, and Circuits"

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Jihwan Kim, Intel, ISSCC 2023 Forum F1.5: Circuit Designs for 200+Gb/s Electrical Transceivers

Ariel Cohen, Intel, ISSCC 2024 Forum F6.3: Beyond 200Gbps Electrical transceivers – Circuit Architecture, Design Implementation and Silicon Results

Heng Zhang, Broadcom, ISSCC 2025 Forum F4.2: High-speed ADCs for 100Gbps+ Wireline Transceivers

E-Hung Chen, MTK, ISSCC 2026 Forum F2.3: State-of-the-Art 200+ Gb/s Electrical and Optical Interconnects


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