DesignCon 2014

Practical Method for Measuring Digital Driver Impedance

Richard Allred, SiSoftrallred@sisoft.com

Sergio Camerlo, Ericsson

Kusuma Matta, Ericsson

Matthew McCarn, Analog Devices, Inc.

Michael Steinberger, SiSoftmsteinb@sisoft.com

Abstract

Knowledge of the data driver output impedance is essential to the analysis high speed data channels, and yet it can be difficult to obtain measured impedance data that meets the needs of system developers, especially for the very highest data rates, and especially under normal operation.

This paper presents a method that uses a TDR test set, a high speed oscilloscope, and two different load impedances to measure the output impedance and voltage waveform at the die for a high speed data driver in normal operation. Fixturing is minimal, and a complete series of measurements can be made in a day. Representative results are presented for several data drivers measured in two different laboratories.

Author(s) Biography

Richard Allred is a Senior Member of Technical Staff at SiSoft. Previously, Richard worked at Inphi where he was responsible for Inphi’s 100G Ethernet PHY (28G per lane) front plane interface. In the course of that work, Richard contributed to IEEE 802.3 and OIF-28G-VSR standards discussions on next generation Ethernet. Before that he worked at Intel, contributing to signal integrity methodology and tool development for GDDR5/DDR3. Richard received his MSEE from the University of Utah, and has 4 publications.

Sergio Camerlo is an Engineering Director with Ericsson Silicon Valley (ESV), which he joined through the Redback Networks acquisition. His responsibilities include the Chassis/Backplane infrastructure design, PCB Layout Design, System and Board Power Design, Signal and Power Integrity. He also serves on the company Patent Committee and is a member of the ESV Systems and Technologies HW Technical Council. In his previous assignment, Sergio was VP, Systems Engineering at MetaRAM, a local startup, where he dealt with die stacking and 3D integration of memory. Before, Sergio spent close to a decade at Cisco Systems, where he served in different management capacities. Sergio has been awarded fourteen U.S. Patents on signal and power distribution, interconnects and packaging.

Kusuma Matta has been working with Ericsson Inc. as a hardware engineer in the field of signal integrity engineering since 2007. Prior to Ericsson, she worked at LSI also in the field of signal integrity engineering. Her research interests include signal integrity for SerDes and DDR interfaces, board and package level SI optimizations, and VNA and TDR measurements. Kusuma has M.S. in Electrical Engineering from University of South

Carolina and B.S. in Electronics and Communications Engineering from JNTU (Jawaharlal Nehru Technological University), Kakinada, India.

Matthew McCarn is an engineer at Analog Devices, Inc., responsible for supporting field application engineers and customers. For the last two years, he has been generating training and enabling simulations for JESD2048 serial interface products. Prior to that, he spent six years enabling the use of ADI’s HDMI products. Matthew holds a BS in Electrical Engineering from North Carolina State University.

Michael Steinberger, Ph.D., Lead Architect for SiSoft, has over 30 years experience designing very high speed electronic circuits. Dr. Steinberger holds a Ph.D. from the University of Southern California and has been awarded 14 patents. He is currently responsible for the architecture of SiSoft's Quantum Channel Designer tool for high speed serial channel analysis. Before joining SiSoft, Dr. Steinberger led a group at Cray, Inc. performing SerDes design, high speed channel analysis, PCB design and custom RAM design.

Problem Description

When designing very high data rate system interconnects, it can be important to have accurate data on the output impedance of the data drivers. This can be especially important when there is a significant discontinuity in the transmission path relatively close to the driver because any standing waves between the driver and the discontinuity can become the dominant impairment in the data link [1], [2].

Unfortunately, the impedance data that is available for many data drivers does not meet the needs of the system developer. This is especially the case for very high data rates because accurate impedance data at high frequencies is seldom available.

The challenges to be overcome are

1. The driver must be characterized in normal operation- that is, while it is driving a typi-cal data pattern into a matched load at its design DC bias point. The data must account for the impedance of the driver during switching events.

2. The impedance data should be derived from laboratory measurements.

3. The measurement environment must have only minimal effect on the device under test. This can be problem if an external signal such as the swept sine wave for a VNA is used to measure the impedance in that the driver’s output signal can interfere with the measurement signal.

4. The impedance data should account for the effects of the package. Ideally, the imped-ance should be measured at the die interconnect and the package model provided sepa-rately.

5. The measurement method should be able to separate linear from nonlinear effects. Most high data rate design methodologies approximate the data driver as a linear device even though it’s a switching device; so it’s important to know the extent to which this approximation is accurate.

6. It would be desirable if the measurement required only limited fixturing in that it would then be practical to measure more devices under a wider range of conditions.

7. It would be desirable if, in addition to producing the device impedance, the measure-ment produced the voltage waveform at the die interconnect.

Solution Overview

This paper presents a method which meets these challenges by using the driver’s output signal as the test signal. Time domain waveforms are measured for two different load impedances (as shown in Figure 1), thus defining the impedance scale. The transmitter impedance is then inferred from the difference in the waveforms from the two measure-ments. Note that in an actual measurement, it’s often necessary to insert AC coupling in the measurement path to maintain the correct DC bias at the transmitter.

This method is demonstrated by presenting data for one example driver. However, this method has been applied to several different drivers, measured in at least two different

laboratories. One of these laboratories is at a system development company, thus demon-strating that it is practical for system developers to make these measurements when they are unable to get the required data from their device supplier.

FIGURE 1. Transmitter impedance measurement

In Figure 1, the load impedance RL is specifically identified as the input port of the oscil-loscope. Using the input port of the oscilloscope as the load is preferable to approaches based on high impedance probes, in that the oscilloscope input port offers a better imped-ance match, the response of the oscilloscope input port is better calibrated, and using the oscilloscope input port is easier to implement.

FIGURE 2. Transmitter impedance measurement with measurement network

Vout1(t)+

-

Vout2(t)+

-Rm ~250Ω

Rm ~250Ω

RL

RL

RL

RL

(Sampling oscilloscope port)

Measurement 1

Measurement 2

Vout1(t)+

-RL

RL

S1

Vpad1(t)

Ipad1(t)

Vout2(t)+

-RL

RL

S2

Vpad2(t)

Ipad2(t)

Time domain reflectometry (TDR) measurements are used to characterize the interconnect network so that the interconnect network can be de-embedded from the measurement, thus determining the voltage and current at the connection to the die. The associated circuit model is shown in Figure 2.

In Figure 2, the difference in S parameters is due to the presence of the shunt resistors in the second measurement. The S parameters are determined through the TDR measure-ments so that the analysis procedure can infer Vpad and Ipad from Vout.

There are several considerations that are critical to the analysis procedure, and should therefore be addressed by the measurement method:

• The data pattern should have a relatively uniform spectral density up to as high a fre-quency as possible, so as to maintain a relatively high signal to noise ratio at all of the frequencies of interest. Maximizing the data rate helps in this regard, but it’s also important to choose a data pattern with relatively high transition density and a variety of run lengths. A PRBS data pattern is a good choice for this application. Such a pattern also assures that the data pattern during is at least somewhat representative of the data expected during normal operation.

• The amplitudes of the waveforms with and without shunt resistor will be nearly the same. Thus, this calculation necessarily involves small differences between larger num-bers. Lower values of shunt resistance will produce larger differences, which will there-fore improve the accuracy of the calculation. The shunt resistance should therefore be the lowest value that will not significantly affect the driver bias point.

• The de-embedding process depends on having accurate S parameters for the measure-ment network. This is a challenge even with the best test equipment and the most sophisticated fixturing. It is an even bigger challenge when making measurements that are practical in a system laboratory. The measurement and analysis methods therefore are designed to extract the most accurate S parameters possible from the TDR data.

• The precise time alignment between the waveforms without and with shunt resistor is critical. Differences of a couple of picoseconds will shift the calculated reflection coef-ficient from plausible to implausible, or vice versa. Since the waveforms are not auto-matically aligned in the measurement procedure, the analysis procedure must align the waveforms correctly. The correct time alignment is obtained by choosing an alignment time that minimizes the average difference in group delay across the frequency band of interest.

Even if all of these considerations are addressed as effectively as possible, this approach does eventually become limited by the problem of small differences between waveforms. Most digital drivers have a parasitic shunt output capacitance that causes their output impedance to go down at higher frequencies. The load impedance, with or without shunt resistor, tends to stay comparatively constant with frequency. Thus, the difference between the waveforms without and with shunt will become even smaller as the frequency increases, thus producing less and less accurate results.

While more sophisticated methods have proven effective when applying this method to waveforms from circuit simulators, the most effective approach to date for measured waveforms is to identify an average amplitude ratio between the waveforms without and with shunt resistor, and use that ratio to calculate an output resistance. The reactive com-ponent of the driver is then derived from TDR measurements made on the unpowered driver. There is admittedly some possibility that this method will fail to accurately identify the effect of the depletion region capacitance of the output transistors; however, it’s the best method we currently have.

For circuits with significant shunt output capacitance, it may also be effective to apply this method using a combination of shunt resistance and capacitance instead of simply shunt resistance. This would tend to increase the difference in load impedances at higher fre-quencies without unduly perturbing the driver’s DC bias point. Such an approach is a potential topic for future work.

Measurement Method

The measurements are made using a circuit board that can drive a pseudo-random bit stream (PRBS7 or PRBS9) data pattern through the driver. The output of the driver is con-nected through coaxial cables to the matched input ports of an oscilloscope, using either connectors on the board or a probe fixture. An evaluation board works very well for this purpose, but measurements were also made on a spare driver on a system board.

For each driver configuration, two time domain waveforms are measured using either a sampling or a real time oscilloscope. For one of these waveforms, the matched impedance inputs to the oscilloscope are the load for the driver. For the second waveform, a shunt resistor is added to the circuit, preferably as close to the driver as possible.

FIGURE 3. Shunt resistor mounting options

In some cases, a skilled technician has soldered the resistor between the true and comple-ment pads on the circuit board. In other cases, shunt resistors to ground were mounted in coaxial adaptors inserted at the coaxial connectors on the board under test. Figure 3 illus-trates several of the options we have used to date.

500 ohms is a typical value for a shunt resistor mounted differentially between true and complement pins, although values as low as 100 ohms would probably produce valid results.

The steps of the data collection are:

1. Measure the TDR of the measurement cables driving an open circuit or short circuit.

2. With the driver powered off, measure the TDR of the measurement cables connected to the board under test, both with and without the shunt resistance. Note that if the shunt resistor is being soldered to the board under test, the measure-ment with shunt resistor will usually be made later in this procedure, after all the wave-forms without the shunt resistor have been made.

3. Connect the measurement cables to matched input ports of the oscilloscope. Turn on the power to the driver, and set the data pattern to either PRBS7 or PRBS9 at the high-est data rate the driver will support.

4. Measure at least one full iteration of the data pattern without shunt resistor. The results will be much more accurate if the oscilloscope uses pattern locking to obtain the aver-age over many iterations of the data pattern.

5. Measure at least one full iteration of the data pattern with shunt resistor inserted in the circuit. Again, pattern locked measurements are preferred.

This sequence of measurements typically takes less than a day, even when there are many driver configurations to be measured.

Analysis Procedure

Core Analysis

The central concept in the analysis procedure is to determine an output impedance from the waveforms measured while driving two different load impedances, given the assump-tion that the driver is linear. This is illustrated in simplified form in Figure 4.

FIGURE 4. Transmitter impedance measurement

Figure 4 shows the Thevenin equivalent circuit for the driver. Since the circuit is assumed to be linear and time-invariant, the analysis can be performed in the frequency domain.

(EQ 1)

(EQ 2)

(EQ 3)

(EQ 4)

(EQ 5)

(EQ 6)

Note that the output impedance from Equation 6 can be substituted back into Equation 3 to obtain the open circuit output voltage.

Vout1(t)+

-

Vout2(t)+

-

Rm

ZL

ZL

Zout

Zout

Vopen

Vopen

Vout1 ω( ) Vopen ω( )ZL ω( )

Zout ω( ) ZL ω( )+-----------------------------------------=

Vout2 ω( ) Vopen ω( )ZL ω( ) Rm||

Zout ω( ) ZL ω( ) Rm||+-------------------------------------------------------=

Vout1 ω( )Zout ω( ) ZL ω( )+

ZL ω( )----------------------------------------- Vopen ω( ) Vout2 ω( )

Zout ω( ) ZL ω( ) Rm||+ZL ω( ) Rm||-------------------------------------------------------= =

Vout1 ω( )Zout ω( )ZL ω( )

------------------- 1+⎝ ⎠⎛ ⎞ Vout2 ω( )

Zout ω( )ZL ω( ) Rm||----------------------------- 1+⎝ ⎠⎛ ⎞=

Zout ω( )Vout1 ω( )

ZL ω( )----------------------

Vout2 ω( )ZL ω( ) Rm||-----------------------------–⎝ ⎠

⎛ ⎞ Vout2 ω( ) Vout1 ω( )–=

Zout ω( )Vout2 ω( ) Vout1 ω( )–

Vout1 ω( )ZL ω( )

----------------------Vout2 ω( )

ZL ω( ) Rm||-----------------------------–----------------------------------------------------------=

Analysis Overview

The remainder of the analysis procedure either prepares the load impedances and voltage waveforms for this calculation or derives relatively straightforward products from the resulting output impedance and open circuit waveform. Most of the effort is devoted to developing as accurate a model of the measurement circuit as possible.

The steps of the analysis procedure are

1. From the TDR of the cable ending in an open circuit, determine a loss vs. frequency for a model of the cable. This loss should be such that a TDR of the model matches the slope of the open circuit at the end of the measured TDR trace.

2. From the TDR of the board under test without and with shunt resistor, create a board model whose TDR matches the measured TDR. Removing the cable loss determined in the previous step helps to make this board model more accurate. In this paper, we will present a method for removing the cable loss and other artifacts of the TDR test set.Typically, the unpowered driver is an open circuit, and so it is possible to create an interconnect model that goes all the way to the die connection on the device.The interconnect model can be expressed in any form that is equivalent to S parame-ters.

3. Given the measured time domain waveforms and the S parameters of the interconnect network without and with shunt, solve for the voltage waveform at the die of the device under test. One way to do this is to transform the S parameters to generalized circuit (ABCD) matrices. Since the load impedance (and therefore the current at the load) is known, the calculation is direct.

4. Time align the voltage waveforms at the die of the device under test.

5. Given the impedance presented to the driver without and with shunt and the voltage waveforms at the driver, solve to obtain a Thevenin equivalent circuit for the driver out-put, including output impedance.

6. Calculate the S parameters of the driver output port from the output impedance of the Thevenin equivalent circuit.

7. Assuming that the data pattern was driving a linear process, perform a least mean squared fit to the measured voltage waveform. Any difference between the linear LMS fit waveform and the calculated waveform is an indication of some form of nonlinear behavior in the driver.

Circuit De-embedding

For the sake of clarity, this description of the circuit de-embedding process will present only the single ended case. Differential waveforms are usually the only data available anyway, and one must make some assumption about the common mode behavior. The usual assumption is that the true and complement pins of the driver are independent, so the single ended approximation is the one that’s used. This analysis can readily be extended to

handle the case of completely independent measurements of the true and complement waveforms for both loading conditions. However, that extension does not yield any additional insights.

Note that while this method was originally developed to analyze measured data, it has to date produced useful results primarily when working with waveforms from circuit simulators. It is presented here for the sake of completeness. For measured data, Equation 6 has usually produced more reliable results.

This treatment is based on the use of generalize circuit matrices (ABCD matrices). Given S parameters that describe a two or four port network, the conversion from S parameters to ABCD matrices is well known, though somewhat complex computationally. Conversion routines are available in several software packages.

Note that using S parameters directly is not as straightforward as would first appear. While the reflection coefficients in the S parameters will provide the load impedance at the pad in a relatively direct way, one cannot simply invert S12 to get the voltage waveform at the pad.

Given an ABCD matrix describing the loading condition for the first

measurement, the voltage and current at the driver pad are

(EQ 7)

where is the input impedance of the oscilloscope. Similarly, for measurement 2,

(EQ 8)

The solution is then

(EQ 9)

A1 ω( ) B1 ω( )

C1 ω( ) D1 ω( )

Vpad1 ω( )

Ipad1 ω( )

A1 ω( ) B1 ω( )

C1 ω( ) D1 ω( )

Vout1 ω( )

Vout1 ω( )Z0

----------------------–=

Z0

Vpad2 ω( )

Ipad2 ω( )

A2 ω( ) B2 ω( )

C2 ω( ) D2 ω( )

Vout2 ω( )

Vout2 ω( )Z0

----------------------–=

Zout ω( )A1 ω( )

B1 ω( )Z0

---------------+⎝ ⎠⎛ ⎞Vout1 ω( ) A2 ω( )

B2 ω( )Z0

---------------+⎝ ⎠⎛ ⎞Vout2 ω( )–

C2 ω( )D2 ω( )

Z0----------------+⎝ ⎠

⎛ ⎞Vout2 ω( ) C1 ω( )D1 ω( )

Z0----------------+⎝ ⎠

⎛ ⎞Vout1 ω( )–--------------------------------------------------------------------------------------------------------------------------------------------=

Waveform De-embedding

When interpreting TDR data, it is often the case the upstream impairments make it more difficult to interpret the reflections due to a given element in the transmission path. It would be nice to have a discplined method for removing these impairments from the data. The impairments to be addressed are

• The stimulus applied by the TDR test is not an ideal step response. It has a non-zero rise time and may include some overshoot or ringing.

• The measurement head of the TDR test set has a finite bandwidth.

• The measured data includes some amount of noise. For the sake of this discussion, this noise will be assumed to be additive white Gaussian noise (AWGN).

• The measurement cables introduce a frequency dependent insertion loss.

In this paper, we refer to the process of minimizing the effect of these impairments as “waveform de-embedding”, even though that term can be easily confused with the more common “circuit de-embedding”. Choice of a less ambiguous name for this process is for further study.

The goal is to obtain a minimum mean square error estimate of the ideal TDR response. We found, however, that this problem is not quite tractable, and so we chose to minimize the mean square difference between our model of the TDR measurement and what our the-ory predicts that we should have measured in the absence of noise. In other words, we need the model to match not only the data obtained from a single performance of a mea-surement, but all performances of the same measurement.

Given a TDR (generated step) stimulus waveform , there exists an impulse response and a resulting TDR response waveform such that

(EQ 10)

where denotes the convolution operator.

Equivalently, in the frequency domain

(EQ 11)

However, neither nor are directly available; so solving Equation 11 directly is not a practical option. Rather, what can be available are measured waveforms that include the effects of bandwidth limitation and measurement noise. The measured stimulus wave-form and corresponding response waveform can be expressed as

(EQ 12)

(EQ 13)

ϕ t( )h t( ) ψ t( )

ψ t( ) h t( ) ϕ t( )⊗=

⊗

Ψ ω( ) H ω( )χ ω( )=

ϕ t( ) ψ t( )

x t( ) y t( )

x t( ) hm t( ) ϕ t( )⊗ n1 t( )+=

y t( ) hm t( ) ψ t( )⊗ n2 t( )+=

where is the impulse response of the measurement, and and are

assumed to be independent samples of the same noise process , conforming to assumption 3. above.

The equivalent frequency domain equations are

(EQ 14)

(EQ 15)

Since we expect to represent a bandwidth limitation while we expect to have a much broader bandwidth, we chose to produce an estimate using a simple real valued fre-quency domain weighting factor . That is,

(EQ 16)

The intent is to compute a precise transfer function at frequencies for which the signal to noise ratio is large, but to taper the estimated transfer function to zero at frequencies for which the signal to noise ratio is small.

To minimize the mean squared error

(EQ 17)

the optimal weighting factor is

(EQ 18)

This result behaves as intended, in that it produces a meaningful result for high signal to noise ratio, but reduces the estimate to zero as the signal to noise ratio becomes smaller.

To apply this result, one must supply estimates for the variables in the equation. For TDR measurements, the device under test usually introduces only small perturbations, and so

it’s reasonable to choose . The spectral density of the stimulus/measurement,

, usually exhibits a well defined low pass characteristic for which a simple two pole or four pole low pass filter approximation should serve well enough. Similarly,

the noise floor is readily apparent at frequencies above the stimulus/mea-surement bandwidth.

hm t( ) n1 t( ) n2 t( )

n t( )

X ω( ) Hm ω( )χ ω( ) N1 ω( )+=

Y ω( ) Hm ω( )Ψ ω( ) N2 ω( )+ Hm ω( )H ω( )χ ω( ) N2 ω( )+= =

hm t( ) n t( )

A ω( )

H ω( ) A ω( )Y ω( )X ω( )-------------=

E H ω( )χ ω( ) H ω( )X ω( )–2

( )

A ω( )Hm ω( )H ω( )χ ω( ) 2

Hm ω( )H ω( )χ ω( ) 2 E N2 ω( ) 2( )+--------------------------------------------------------------------------------------=

H ω( ) 2 1=

Hm ω( )χ ω( ) 2

E N2 ω( ) 2( )

Results

This section provides an example of the transmitter impedance measurement process from beginning to end. The device under test was a spare driver on a test board, so it was not connected to any routing. The pads on the opposite side of the board from the device were contacted using a four pin PCB probe. To make the measurements with shunt resistor, a 500Ω resistor was soldered on one side of the true and complement pads of the device, and the PCB probe contacted the other side of the pads.

• The stimulus, bandwidth and noise of the TDR test set are determined, resulting in a weighting function to be used in the waveform de-embedding process.

• The layers of the TDR response are peeled away one at a time, resulting in a determina-tion of the measurement cable loss, probe loss/response, and PCB/package/shunt resis-tor TDR response. This data was used to create a model of the measurement environment up to the die bumps on the driver.

• The measurement circuit is (circuit) de-embedded from time domain waveforms with-out and with shunt resistor, producing the voltage waveforms at the die bump of the driver.

• The time domain waveforms are examined for the effects of driver swing setting and driver nonlinearity.

• The amplitude ratio without and with shunt resistor is used to determine the driver dif-ferential output resistance as a function of driver swing setting.

• The driver differential output resistance is combined with the PCB/package model to determine the reflection coefficient vs. frequency of the driver at the interface to the PCB routing.

TDR Data

Figure 5 shows all of the TDR waveforms that were measured.

• The total TDR waveform from TDR stimulus to measurement cable open circuit was measured in a separate laboratory session after the need for this data was identified. Thus, it has a different start and stop time from the rest of the TDR data.

• A TDR waveform was measured for the measurement cable and open circuited PCB probe.

• TDR waveforms were measured for the unpowered device under test without and with shunt resistor

Figure 6 is a magnified view of the same data. One of the unusual characteristics of this driver is that it presents nearly a matched load at its output terminals when it is powered down. We therefore assumed that the last impedance transition before the TDR waveform achieved steady state was the location of the driver’s bumps at the interface between the die and the package.

FIGURE 5. Measured TDR waveforms

FIGURE 6. Magnified view of TDR waveforms

Figure 7 shows the magnified TDR traces for a more typical device. In this case, the device under test is mounted to an evaluation board with SMA connectors. When required, the shunt resistor was soldered near the AC coupling capacitors. In this case, the location of the driver die bump is much more readily apparent, and the pronounced low impedance response just before the die bump is most likely the parasitic capacitance of the ESD protection device. We included this parasitic capacitance in the device model rather than the package model when we modeled the impedance of this device.

PCB Pads Driver Die Bump??

FIGURE 7. Magnified view of TDR waveforms for different test board and device

TDR Calibration

For Figure 8 the open circuited cable response in Figure 5 was modified to contain only the stimulus response at the earlier times in the waveform (up to about 4ns), and then extended with a constant value, thus removing the response from the open end of the cable. This stimulus response was then transformed to the frequency domain, and the resulting spectrum (in RED) compared to the spectrum (in BLACK) for an ideal step response with a transition time at exactly the same time as that of the stimulus. The differ-ence between these two spectral densities is therefore an indication of the departure of the TDR test set from ideal behavior.

In Figure 8, the spectral density of the actual stimulus at first drops away from that of the ideal response, indicating some bandwidth limitations in the step generator and/or the measurement head. For the measurements reported in this paper, this response was mod-eled as the concatenation of two two-pole Butterworth filters with a 3dB bandwidth of 22 GHz. In measurements using other equipment, the 3 dB bandwidth was 17 GHz.

The stimulus spectrum then assumes a more or less constant value at higher frequencies. This is assumed to be the noise floor of the measurement.

Figure 8 also shows the fit of a model of the stimulus spectrum (in BLUE) resulting from the combination of the Butterworth filters and the noise floor. This model was then used to calculate the weighting function used when applying Equation 16 to the de-embed-ding of subsequent waveforms.

The weighting function is shown in Figure 9.

Driver die bump

ESD protection devicecapacitance

Shunt resistorlocation

AC couplingcapacitors

A ω( )

FIGURE 8. TDR calibration for bandwidth and noise

FIGURE 9. TDR weighting function

TDR De-embedding

The waveform de-embedding process was applied to the open circuited cable waveform in Equation 5, thus removing the limitations of the step generator and measurement head as much as possible. The resulting step response was then transformed to the frequency domain and its spectrum compared to that of an ideal step response with the same amplitude and transition time, as shown in Figure 10.

Noise floor

Measurementbandwidth rolloff

Figure 10 shows that the spectral density gradually falls away from the ideal spectral density, reaching a difference of about 6 dB at 15 GHz. Considering that a TDR measurement is a round trip measurement, the associated cable loss is about 3 dB at 15 GHz. This value is more or less consistent with available commercial data, and so the cable model for this analysis was adjusted to exhibit this loss.

FIGURE 10. Measurement cable loss

Since our measurement of the open circuited probe did not include the stimulus, we used the de-embedded open cable response from the open probe response. The result is shown in Figure 11. The buildup of measurement noise is clearly evident in this result. However, within the apparent accuracy of the measurement, it appears that the probe can be consid-ered to be transparent.

FIGURE 11. De-embedded probe response

The original measured open circuited probe response was truly the stimulus for the mea-surement of the response for the PCB, package, shunt resistor (when present) and unpow-ered driver. It was therefore used in the de-embedding process to obtain a higher resolution TDR response for the device under test, as shown in Figure 12.

Figure 12 also shows the de-embedded version of the open circuited probe. Note that there is some ringing both before and after the open circuit itself. These are artifacts of the waveform de-embedding process. If the weighting function used were something like a Bessel-Thompson response, then there would be no ringing. However, since the weighting function shown in Figure 9 has a flatter passband and sharper rolloff than a Bessel-Thompson filter, there is some distinct ringing present. These artifacts must be considered when interpreting the de-embedded response. In this case, we assumed that the negative transition before the interface with the PCB and half of the positive response after that were de-embedding artifacts. This was probably a conservative interpretation in that the discontinuity at the PCB interface is not as severe as the probe’s open circuit.

FIGURE 12. De-embedded test board TDR response

The waveforms in Figure 12 were used to create a circuit model of the PCB and package. The procedure was essentially a manual form of impedance unrolling, in that the model consists of sections of transmission line that correspond exactly to the lengths and imped-ances in the de-embedded waveforms. Length differences of 0.01” were clearly visible in the modeling. The shunt resistor was modeled as a 500Ω resistor in parallel with a 30fF parasitic capacitance. There was no need to adjust the resistance value. The unpowered driver was modeled as a 53.5Ω resistor to ground on both the true and complement pins.

Figure 13 compares the TDR for the resulting circuit models, without and with shunt resistor, to the de-embedded waveforms in Figure 12. We believe that the models match the measured data within experiment error.

FIGURE 13. Test board model vs. de-embedded measured data

Time Domain Waveforms

Figure 14 shows an example of the time domain waveforms measured without and with shunt resistor for a single gain setting (“main” = 45). In this figure, it appears that the waveform with shunt resistor is equal to the waveform without shunt times a constant factor. This was not expected at first, but we have seen this characteristic in the data measured on several different drivers from different companies and measured in different laboratories. It is extremely useful in that it has allowed us to use Equation 6 to produce estimates of output resistance which have been the most consistent and reliable results from this measurement procedure. This will be addressed further in the discussion of driver impedance results.

FIGURE 14. Measured waveform without and with shunt resistor. Swing = 45

The model from Figure 13 and the circuit de-embedding procedure were used to estimate the waveform at the driver die bump, as shown in Figure 15. This figure also shows the waveform at the same location for the driver model, using the same interconnect model and the output resistance reported below for “main”=45. There seems to be a reasonable correlation between the two waveforms.

FIGURE 15. De-embedded measured waveform vs. model. Without shunt. Swing=45

Figure 16 shows a sweep of the voltage waveform at the driver die bump as a function of swing setting. The observed amplitude variation was not nearly as large as the device data sheet had led us to expect. We see this as a clear demonstration of the value this measure-ment procedure offers the system developer.

FIGURE 16. De-embedded waveform sweep

We created linear approximation to the waveform without shunt in Figure 14 by calculat-ing a pulse response from the waveform and then linearly modulating that pulse response with the original data pattern. The procedure for calculating the pulse response can be rig-orously proven mathematically to produce a minimum mean square error estimate. Figure 17 compares the linear fit to the original waveform.

We have performed this exercise many times on many different waveforms and gotten uniformly consistent results. The nonlinear artifacts we have observed are

• DC offset

• Clock based duty cycle distortion (DCD). This is typically for a half rate clock.

• Data based DCD

• Above a frequency equal to the data rate, the spectral density does not seem to vary with load impedance in a way that is consistent with a linear model. Since the spectral densities in this frequency region are relatively small to begin with, we have not attempted to draw any conclusions.

The data based DCD has always been distinctly measurable, but quite small. DC offset and clock based DCD have varied between very low values to values that were quite sig-nificant [3]. To date, we have observed no other nonlinear effects. A complete demonstra-tion of the validity of a linear driver model, would require that we derive waveforms from open circuit voltages and output impedances and compare them directly to measured waveforms; and we haven’t quite done that. However, this result comes very close.

FIGURE 17. Measured waveform vs. linear approximation

Driver Impedance

For each swing setting, we identified a constant multiplier between the amplitude without shunt and with. A spectral analysis indicated that this multiplier is very nearly constant all the way to a frequency equal to the data rate. Above that frequency, the spectral density falls faster for the waveforms with shunt than it does for the waveforms without. The impedance results may therefore not be valid for frequencies above the data rate.

We used these amplitude ratios and Equation 6 to calculate a differential output resistance. The results are shown in Figure 18. From these results, it appears that although the swing setting doesn’t seem be very successful in varying the swing very much, it certainly does have an effect on the output resistance. From these results, it appears that a swing setting of “main”=45 should produce the best link performance.

FIGURE 18. Driver differential source resistance vs. swing setting

Finally, we used the output resistance from Figure 18 with the interconnect model from Figure 13 to estimate the reflection coefficient at the PCB pads where the waveforms were measured. The result is shown in Figure 19. Based on the results in Figure 18, we expect that changing the swing setting will shift the reflection coefficient to the left or right, with lower swing settings going to the right and higher swing settings to the left (by quite a lot at the highest swing settings).

0

20

40

60

80

100

120

140

160

30 35 40 45 50 55 60 65

Zout

main (swing control parameter)

FIGURE 19. Driver reflection coefficient, Swing=45

Conclusions

Using a combination of TDR measurements and time domain waveforms measured with-out and with shunt resistor, it is possible to measure the output impedance vs. frequency and voltage waveform at the die connection of a data driver. Although the data reduction involves a number of steps, the measurements can be made is less than a day using equip-ment that is typically available in a system lab. This procedure meets all of the challenges listed in the introduction to this paper:

1. The driver is characterized in normal operation using a data pattern that resembles typ-ical data traffic.

2. The impedance data is derived from laboratory measurements that can be made by a system developer as well as a device supplier.

3. The output of the driver is used to measure the impedance. No external signals are required.

4. The output impedance is measured at the die interconnect of the device.

5. The measurement method separates linear from nonlinear effects, thus evaluating the approximation of a driver as a linear circuit.

6. The measurement procedure requires minimal fixturing.

7. The measurement produces the voltage waveform at the die interconnect as well as the device impedance.

We have also presented methods for de-embedding both circuit effects and waveform effects from the measured data.

Based on our experience to date, we conclude that, except for linear parasitics attached to the output of the driver, drivers tend to exhibit a constant output resistance, resulting in amplitudes that vary in a broadband way as a function of load impedance. The resulting amplitude factor has provided a relatively simple and reliable way to estimate driver out-put impedance.

References1. Steinberger, Wildes, Higgins, Brock and Katz, “When Shorter Isn’t Better”,

DesignCon2010, February 2, 2010.

2. Telian, Camerlo, Kirk, "Simulation Techniques for 6+ Gbps Serial Links", DesignCon 2010, February 2, 2010.

3. Steinberger, Wildes, Ekholm, Svee, “Measurement-based simulation: increasing IBIS-AMI model accuracy with data from lab measurements”, paper 9-WA3, DesignCon2013, February 1, 2013.