serdes.ChannelLoss

Create simple lossy transmission line model

Description

The serdes.ChannelLoss System object™ constructs a lossy transmission line model for use in the SerDes Designer app and other exported Simulink^® models in the SerDes Toolbox™. For more information, see Analog Channel Loss in SerDes System.

To construct the loss model from channel loss metric:

1. Create the serdes.ChannelLoss object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

ChannelLoss = serdes.ChannelLoss

ChannelLoss = serdes.ChannelLoss(Name,Value)

Description

ChannelLoss = serdes.ChannelLoss returns a ChannelLoss object that modifies an input waveform with a lossy printed circuit board transmission line model according to the method outlined in [1].

ChannelLoss = serdes.ChannelLoss(Name,Value) sets properties using one or more name-value pairs. Enclose each property name in quotes. Unspecified properties have default values.

Example: ChannelLoss = serdes.ChannelLoss('Loss',5,'TargetFrequency',14e9) returns a ChannelLoss object that has a channel loss of 5 dB at 14 GHz.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Loss — Channel power loss at target frequency

8 (default) | real scalar

Channel loss at the target frequency, specified as a real scalar in dB.

Data Types: double

TargetFrequency — Frequency of desired channel loss

1e10 (default) | positive real scalar

Frequency for the desired channel loss, specified as a positive real scalar in Hz.

Data Types: double

dt — Sample interval

1e-12 (default) | positive real scalar

Sample interval in s, specified as a positive real scalar.

Data Types: double

Zc — Differential characteristic impedance

100 (default) | positive real scalar

Differential characteristic impedance of the channel, specified as a positive real scalar in ohms.

Data Types: double

TxR — Single-ended impedance of transmitter analog model

50 (default) | nonnegative real scalar

Single-ended impedance of the transmitter analog model, specified as a nonnegative real scalar in ohms.

Data Types: double

TxC — Single-ended capacitance of transmitter analog model

1e-12 (default) | nonnegative real scalar

Single-ended capacitance of the transmitter analog model, specified as a nonnegative real scalar in farads.

Data Types: double

RxR — Single-ended impedance of receiver analog model

50 (default) | nonnegative real scalar

Single-ended impedance of the receiver analog model, specified as a nonnegative real scalar in ohms.

Data Types: double

RxC — Capacitance of receiver analog model

1e-12 (default) | nonnegative real scalar

Capacitance of the receiver analog model, specified as a nonnegative real scalar in farads.

Data Types: double

RiseTime — 20%−80% rise time of stimulus input

1e-11 (default) | positive real scalar

20%−80% rise time of the stimulus input to transmitter analog model, specified as a positive real scalar in seconds.

Data Types: double

VoltageSwingIdeal — Peak-to-peak voltage at input of transmitter analog model

1 (default) | positive real scalar

Peak-to-peak voltage at the input of transmitter analog model, specified as a positive real scalar in volts.

Data Types: double

EnableCrosstalk — Include crosstalk in simulation

false (default) | true

Set EnableCrosstalk to true to include crosstalk in the simulation. By default, EnableCrosstalk is set to false.

CrosstalkSpecification — Specify magnitude of near and far end aggressors

CEI-28G-SR (default) | CEI-25G-LR | CEI-28G-VSR | 100GBASE-CR4 | Custom

Specify the magnitude of the near and far end aggressors. You can choose to include maximum allowed crosstalk for specifications such as 100GBASE-CR4, CEI-25G-LR, CEI-28G-SR, CEI-28G-VSR, or you can specify your own custom crosstalk integrated crosstalk noise (ICN) level.

fb — Baud rate for ICN calculation

14e9 (default) | positive real scalar

Baud rate used for integrated crosstalk noise (ICN) calculation, specified as a positive real scalar in hertz. fb is the inverse of the symbol time.

Dependencies

This property is only available when EnableCrosstalk is set to true.

Data Types: double

FEXTICN — Desired integrated noise level of far end aggressor

15e-3 (default) | nonnegative real scalar

Desired integrated crosstalk noise (ICN) level of the far end aggressor, specified as a nonnegative real scalar in volts. ICN specifies the strength of the crosstalk.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

Aft — Amplitude factor of far end crosstalk aggressor

1.200 (default) | positive real scalar

Amplitude factor of the far end crosstalk aggressor, specified as a positive real scalar in volts.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

Tft — Rise time of far end crosstalk aggressor

9.6e-12 (default) | positive real scalar

Rise time of the far end crosstalk aggressor, specified as a positive real scalar in seconds.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

NEXTICN — Desired integrated noise level of near end aggressor

10e-3 (default) | nonnegative real scalar

Desired integrated crosstalk noise (ICN) level of the near end aggressor, specified as a nonnegative real scalar in volts. ICN specifies the strength of the crosstalk.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

Ant — Amplitude factor of near end crosstalk aggressor

1.200 (default) | positive real scalar

Rise time of the near end crosstalk aggressor, specified as a positive real scalar in seconds.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

Tnt — Rise time of near end crosstalk aggressor

9.6e-12 (default) | positive real scalar

Rise time of the near end crosstalk aggressor, specified as a positive real scalar in seconds.

Dependencies

This property is only available when EnableCrosstalk is set to true and CrosstalkSpecification is set to Custom.

Data Types: double

Usage

Syntax

y = ChannelLoss(x)

Description

y = ChannelLoss(x)

Input Arguments

x — Input baseband signal

scalar | vector

Input baseband signal.

Output Arguments

y — Estimated channel output

scalar | vector

Estimated channel output that includes the effect of a lossy printed circuit board transmission line model according to the method outlined in Analog Channel Loss in SerDes System.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Processing Ideal Sinusoid Using ChannelLoss Model

This example shows how to process an ideal sinusoidal input waveform with the ChannelLoss model and check that it modifies the amplitude of the waveform in a reasonable way.

Define the system parameters. Use a symbol time of 100 ps with 8 samples per symbol. The amplitude of the input signal is 1 V. The channel loss is 3 dB.

SymbolTime = 100e-12;
SamplesPerSymbol = 8;
a0 = 1;
Loss = 3;

Calculate the sample interval. Define a time vector that is 30 symbols long.

dt = SymbolTime/SamplesPerSymbol;
t = (0:SamplesPerSymbol*30)*dt;

Create the sinusoidal input waveform.

F = 1/SymbolTime/2;      %Fundamental frequency
inputWave = a0*sin(2*pi*F*t);

Create the channelModel object at the specified loss for near ideal transmitter and receiver termination.

channelModel = serdes.ChannelLoss('Loss',Loss,'dt',dt,...
      'TargetFrequency',F,'TxR',50,'TxC',1e-14,... 
      'RxR',50,'RxC',1e-14);

Process the input waveform using the channelModel object.

 outputWave = channelModel(inputWave);

Calculate the output amplitudes.

a1 = max(outputWave);                              %Output amplitude
aideal = a0*10^(-abs(channelModel.Loss)/20);       %Theoretical output amplitude

Generate the frequency response.

s21 = channelModel.s21;
f = (0:length(s21)-1)*channelModel.dF;

Determine the loss at the target frequency of the frequency response.

f1 = find(f>channelModel.TargetFrequency,1,'first');
LossAtTarget = interp1(f(f1-1:f1),db(s21(f1-1:f1)),channelModel.TargetFrequency);

Plot the time and frequency response of the channel model.

tns = t*1e9;
thline = [tns(1),tns(end)];
fghz = f*1e-9;
figure
subplot(211)
plot(tns,outputWave,thline,aideal*[1 1],thline,a1*[1 1],'b--'),
grid on
xlabel('ns'),ylabel('Voltage')
title('Time Response of Channel Model')
legend('Output waveform',...
sprintf('Ideal amplitude: %g mV',round(aideal*1e3)),...
sprintf('Actual amplitude: %g mV',round(a1*1e3)),'Location','southwest')
subplot(212)
plot(fghz,db(s21),...
channelModel.TargetFrequency*1e-9,LossAtTarget,'o')
title('Frequency Response of Channel Model')
legend('S_{21}(f)',sprintf('%g dB @ %g GHz',LossAtTarget,channelModel.TargetFrequency*1e-9))
grid on
xlabel('GHz')
ylabel('dB')

More About

Integrated Crosstalk Noise (ICN)

ICN is a frequency domain metric where the crosstalk is multiplied by a weighting function and then numerically integrated from 50 MHz to the baud rate (f_b). If there are multiple aggressors, their power are summed together before combining with the weighting function.

The time domain signal does not excite all frequencies evenly. The power spectral density (PSD) of a baseband time domain excitation follows a sinc-squared type response. The weighting function mimics the excitation of the PSD and shapes the PSD by including the effects of the receiver bandwidth and the transmitter rise time.

The total ICN is calculated by root-sum-squaring the FEXT ICN and NEXT ICN values together.

$$\begin{array}{l}{W}_{ft}(f)=\left(\frac{A_{ft}^2}{4f_b}\right){\text{sinc}}^2\left(\frac{f}{f_b}\right)\left[\frac{1}{1+{\left(f/f_{ft}\right)}^4}\right]\left[\frac{1}{1+{\left(f/f_{ft}\right)}^8}\right]\\ {\sigma }_{fx}={\left(2\Delta f{{\displaystyle \sum _n{W}_{ft}(f_n)10}}^{-MDFEX{T}_{loss}(f_n)/10}\right)}^{1/2}\\ {\sigma }_{nx}={\left(2\Delta f{{\displaystyle \sum _n{W}_{ft}(f_n)10}}^{-MDNEX{T}_{loss}(f_n)/10}\right)}^{1/2}\\ {\sigma }_x=\sqrt{{\sigma }_{fx}^2+{\sigma }_{nx}^2}\end{array}$$

Algorithms

Creating Transmission Line Model

To obtain a lossy printed circuit board (PCB) transmission line (T-line) model with a given Loss at the TargetFrequency, two T-lines of length 100 mm and 150 mm are created and loss evaluated at the Target Frequency. These two data points are used to extrapolate to the transmission line length needed to achieve the requested loss. The transmission line model is an analytic equation based on the method described in [1].

This transmission line, with the requested loss is then combined with the Tx and Rx single ended termination resistance and capacitance as illustrated below:

Creating Far End Crosstalk

The impact felt on a victim line from a far end crosstalk aggressor is proportional to the rate of change of the aggressor waveform [2]. So, you can estimate the shape of a FEXT time domain signal with the derivative of the through response lossy impulse response.

$$I_{\text{FEXT}}(t)=k_{\text{FEXT}}\frac{dI(t)}{dt}$$

where, k_FEXT is a scale factor that scales the I_FEXT(t) so that it has user specified ICN value.

To calculate the ICN of the signal, transform the signal to frequency domain using Fourier transform.

$$H_{\text{FEXT}}(f)=ℱ\left[I_{\text{FEXT}}(t)\right]$$

The magnitude of the scale factor k_FEXT is: $$k_{\text{FEXT}}(f)=-\frac{IC{N}_{\text{FEXT}}}{\mathbb{I}ℂ{\mathbb{N}}_{\text{FEXT}}\left(H_{\text{FEXT}}(f)\right)}$$,

where $$\mathbb{I}ℂ\mathbb{N}$$ is the integrated crosstalk noise operator.

The sign of k_FEXT is negative since in typical transmission lines in inhomogeneous dielectrics, the inducting coupling is generally greater than capacitive coupling. As a result, the forward crosstalk pulse has the opposite magnitude from the magnitude of the aggressor signal.

Creating Near End Crosstalk

To calculate the near end crosstalk, note that the frequency domain NEXT response is similar in shape (not in magnitude) to the victim's return loss (S₁₁ or S₁₁).

$$H_{\text{NEXT}}(f)=k_{\text{NEXT}}·S_{11}(f)$$

Then the scale factor k_NEXT is: $$k_{\text{NEXT}}=-\frac{IC{N}_{\text{NEXT}}}{\mathbb{I}ℂ\mathbb{N}\left(S_{11}(f)\right)}$$

And the time domain NEXT signal is derived from the inverse Fourier transform.

$$I_{\text{NEXT}}(t)={ℱ}^{-1}\left[k_{\text{NEXT}}·S_{11}(f)\right]$$

References

[1] IEEE 802.3bj-2014. "IEEE Standard for Ethernet Amendment 2: Physical Layer Specifications and Management Parameters for 100 Gb/s Operation Over Backplanes and Copper Cables." https://standards.ieee.org/standard/802_3bj-2014.html.

[2] Stephen Hall and Howard Heck. Advanced Signal Integrity for High-Speed Digital Designs. Hoboken, NJ: Wiley Press, 2009.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

IBIS-AMI codegen is not supported in MAC.

Version History

Introduced in R2019a