IEEE Instrumentation and Measurement Technology Conference Budapest, Hungary, May 21-23, 2001.
Measurement Problems in High-speed Networks Madhavan Swaminathan*, Woopoung Kim*, Istvan Novak + * Georgia Institute of Technology 777, Atlantic Drive, School of Electrical and Computer Engg., Atlanta, GA 30332 - 0250, USA e-mail:
[email protected] + Sun Microsystems, Inc. One Network Drive, Burlington, MA 01803, USA Phone: +1 781 442 0340, Fax: +I 781 442 1575 e-mail:
[email protected] Abstract - Computer hardware and communications network speeds are rising at a steady rate. From Moore’s law we know that the silicon computing power is doubled every 18 month, and especially with the onset of internet, the demand for increasing network bandwidth is also on the constant rise. CPU speeds have recently broken through the IGHz barrier, a d IOGbiu‘sec network connections are becoming common. With the faster clock signals and shrinking silicon dimensions, digital transitions becomefaster, and presently sub-100psec transition times are measured. To save power, but also as a need from the smaller silicon feature sizes, digital voltage swings are becoming smaller. The gigabit signaling techniques combined with dense printed-circuit-board wiring create on-board transmission lines where losses and dispersion must be taken into account. Finally, the low operating voltages and high supply currents create a need for powepdistribution impedances in the milliohm range. As a result, measuring and simulating the signals with several GHz bandwidth, verifiing trace and cable losses and transfer characteristics, measuring power-distribution network impedances creates new challenges. The paper gives an overview of the state-of-the-art measurement solutions for the abovefields. Kevwords - lossy interconnects, powepdistribution network, prameier extvaction.
I. NRODUCTION As the operating frequency of packaging and circuits in digital systems goes over lGHz, the importance of signal and power transmission has been amplified. At low speeds, the signal or power generated by sources can be transmitted by a single conductor line with little consideration to the return path. However, as frequencies go higher, transmission-line consklerations become important. The main parameters for designing the signal transmission lines are Characteristic impedance and propagation constant. The propagation constant can be measured through TRL calibration [ 1][2] [7] or TDWTDT measurement [3]. However, due to the impedance of reference planes, measuring the characteristic impedance is not so easy. The reference impedance after TRL calibration is not 50 ohm but the characteristic impedance of the through structure, which is the object to be measured. Hence, the TRL method produces reflectivity zero since the through transmission line is the same structure with the reference plane. It does not give the characteristic impedance of the transmission lines. Instead, some computa-
tion methods have been used to calculate the characteristic impedance from the measurement of the propagation constant [4]. Until now several methods to directly measure the characteristic impedance has been tried using Vector Network Analyzers.[5][6] [5] claims exact extraction of characteristic impedance using VNA producing complex characteristic im pedances. However, as the curve figures of the extracted characteristic impedance for CPW lines in [5] and [6] show, the extracted Z O needs verification and explanation. Although [5] and [6] show results for CPWs on lossy substrates, the curve shapes are so different that one goes up with frequency and the other down. It is highly dependent on the modeling of the pad transitions. TDR has several advantages over Network Analyzer for measurement of the characteristic impedance. First of all, TDR is instinctive. While [5] gave the imaginary values of the characteristic impedance, [6] did not. The imaginary values around DC can be estimated ftom TDR measurements. Assume that a transmission line has the imaginary values like [5]. Since the transmission line has negative imaginary values around DC, a step pulse inserted by TDR will have an increasing slope with time after a settling time due to the capacitive effect. And simulation and measurements imply that the negative imaginary values around DC are the absolute maximum. Transmission lines with very small imaginary values around DC will have constant values with time after the settling time like a lossless transmission line. Or if a transmission line has positive imaginary values around DC, a step pulse inserted by TDR will also have an increasing slope with time after the settling time. From TDR measurements, the imaginary values of the characteristic impedance can be mstinctively and easily estimated. Since the transmission lines with negative or positive imaginary values of the characteristic impedance around DC affect the signals after settling time, these lines can contribute to signal integrity problems. Second, TDR can use a physical model for pad transitions, which their parameters can be easily extracted without complex mathematics. Finally, the only structure bat needs to design is transmission lines. Additional structures for calibration are not required. All these properties are quite useful for RF and package engineers.
0-7803-6646-8/01/$10.00 02001 IEEE
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Additionally, since inductors are lossy and resonant, extraction of the frequency-dependent properties from TDR can be difficult. We have shown that this is possible using TDR measurement.
A few methods have been developed in the past to extract the frequency response of the DUT using TDR, details of which are available in [3][9]. In [9], Fourier Transform techniques have been used to extract the impulse response of the DUT using the relation
In today’s computing and networking equipment, the power-distribution networks (PDN) have to provide sufficient low impedance over a wide frequency range. Multi-Chip Modules and system printed circuit boards may have twenty or more power-ground plane pairs, with several thousands of bypass capacitors on the boards, aiming for a mid-frequency PDN impedance of a milliohm or less, as shown in [ 131 and [I4]. Whereas measuring small DC resistance values has long been solved, measuring milliohms of impedances in the hundreds of MHz frequency range creates new challenges. R -GC bridges and Impedance Analyzers usually have an equivalent measurement limit of about 100pH, which limit is mostly associated with the calibration and connection difficulty of probes. In this paper we summarize some of the state-of-the-art
measurement/characterization techniques for signal interconnects with TDR and for power-distribution networks with WAS.
B. Calibrationfor TDR
II. INTERCONNECT CHARACTERIZATIONWITH TDR A . Measuremental setup TDR was initially developed for locating faults on long electrical systems such as telephone wires and network lines. TDR represents the reflected time signature of an hcident step waveform that can be used to extract the characteristics of the Device Under Test (DUT), as shown in Fig. 1. TDR measurements display the round trip electrical delay of cables and the DUT. The size of the discontinuity that can be characterized is a function of the risetime of the step pulse. Commercial TDR equipments support a risetime of 25-3Ops with a 250mV amplitude pulse. tr = 25 ps
where H(o) is the impulse response of the DUT, R(o) is the fourier transform of the reflected signal and P(o) is the fourier transform of the incident signal. However, this method did not use calibration structures to de-embed discontinuities and parasitics, resulting in error in the extracted frequency Esponse. In [3], a method was demonstrated for extracting the impulse response through rational functions by using thru and short calibration. In this paper, a method is discussed for extracting the impulse response from TDR measurements by using open, short and load calibration. This method is more robust and produced better results as compared to [3] for extracting the frequency dependent characteristic impedance of transmission lines.
High Frequency measurements require the qecification of reference planes. A DUT is always characterized at or between reference planes for a 1-port or 2-port measurement, respectively. Calibration structures are required to de-embed parasitics and discontinuities from the measurements at the reference planes. Calibration structures such as short, open, load, thru, reflect, line, etc are often used in measurements. De-embedding using a subset of the calibration structures have been developed by the microwave community. For example, calibration usmg short-open-load-thru (SOLT) and thru-reflect-line ( T U ) have been developed for network analysis. In this paper we have used the Short-Open-Load calibration for I-port TDR measurements. As mentioned earlier, the parasitics and other discontinuities affect the accuracy o f the measurements. For a 1-port TDR measurement, an error model using a signal flow graph can be constructed as shown in Fig. 2 [lo]. RF in
Sampling Oscilloscope (Tektronix 118018)
+l-+
+
Fig.2. Error model for calibration
Fig. 1. Experimental setup
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In the Figure, x, y and z are the parameters calculated from the ~ open, short and 50 ohm load calibration measurements. S l l is the response of the DUT and SI1 M is the measured response which includes the parasitic effect caused by error variables, x, y and z. From Fig. 2, using the signal flow graph, the fiequency response of the DUT can be derived as
If the open, short and load measurements are expressed as S I ~ M SllMs O , and Slim respectively, the variables x, y and z in equation ( 2 ) can be computed as :
Once x, y and z are computed, these parameters can be used to calibrate the DUT using equation (2). This is similar to the 1-port calibration method used in a Network Analyzer.
this line has positive imaginary values around DC. The last is a lossy one with only a conductor loss. The conductivity is set to be le5 S/m and the loss tangent is zero. The characteris tic impedance of this line has negative imaginary values around DC. The TDR responses to the lines are presented in Fig. 4. In case of the line with the dielectric loss, the characteristic impedance goes down due to the dielectric loss and the tail of the TDR response goes up with time. For the line with the conductor loss, the characteristic impedance goes up due to the increased impedance of the conductor. And the tail also goes up with time. However, lossless transmission lines don't have any slope, which implies that as the characteristic impedance is closer to real values, the slope of the TDR response approaches to zero. Hence, from TDR measurement of transmission lines, the imaginary values around DC can be roughly estimated. In most transmission lines, the slope is close to zero and the characteristic impedance can be assumed to be real. However, If the ground plane was not homogenous, the slope was observed.[111 A lossy transmission lines with only dielectric loss can be assumed to be real assumed the dielectric loss affects the real characteristic impedance and the slope of the tail is very small. This is very useful for characterizing the transmissionlines on Silicon.
C. Simulation of TDR
- -_ - -
Conductor loss- - - _______________- _- ------------ Conductor loss-
0.6' 0.61
This simulation shows typical TDR responses to lossy transmission lines. The TDR equivalent circuit is shown in Fig. 3 with a lossy microstrip line in HP-ADS.
c
0.5
lossless
0.4 0.3' 0.3
o.
IMeasured point I
o '0
'j
Dielectric loss
......_..,,(~..........,.,.,,,,.......,,I
.,,........1,,.,.......~.1....
-....
a..
,
.
l
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time[ns]
Fig. 4. Simulation of TDR responses to lossy transmission lines
Tr = 30ps vpp = 1v
The reason why the tail goes up for lossy transmission lines is that the reflected signal by the lossy transmission line is positive with both dielectric loss and conductor loss. The signal around DC can be thought as a cosine wave with a period very large. The reflective coefficients for dielectric -loss and conductive-loss lines are within +90 degrees. So the reflected signals have positive-value signals. So the tail goes up.
w = 1.78 mrn Cond = 10e100 Slm L = 10e5 m
Fig.3. Simulated circuit for TDR
The dimensions of the lossy microstrip line are presented. Three cases were simulated. The First is a lossless transmission line. The conductivity of metals is set to be very large and the loss tangent ofthe dielectric zero. The second is a lossy one with only a dielectric loss. The conductivity is set to be very large and the loss tangent 0.1. The characteristic impedance of
For RF and Package designers, the imaginary values of the Characteristic impedance are not desirable values. For digital circuits, the imaginary values around DC increase the signal level with time, which can contribute to the signal integrity problem of the circuits. Good transmission lines should have
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only real-value characteristic impedances. This aspect must be taken into account when designing transmission lines. This is easily observed in TDR measurements.
Characteristic impedance [ohm]
D. Extraction of the characteristic impedance
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A microstrip transmission line was measured with metal thickness 17 mils, metal width 10 mils, and dielectric thickness 30 mils. It consists of a line above a ground plane with a groundsignal-ground (GS-G) launching pad at the input end. The reference plane is at the input end of the microstrip line before the launching pad. However, to accurately extract the frequency-dependent characteristic impedance of the micmstrip line, the parasitics associated with the launching pad have to be de-embedded. Here four measurements were only performed because the delay between Open and Short standard is not severe, However, generally five measurements are recommended, that is, Open, Short, Load, A shorted transmission line, and DUTs to compensate the delay between Open and Short for probes.
30 .
!
Quaskstatic approximation
............................................................................
25
20 15
ZO is valid from DC to >..........................................................................
-
.
'"0
1
2
3
4
5
6
7
8 9 10 Freq[GHz]
Fig. 6. Frequency-dependent characteristic impedance
E. Embedded inductor Since inductors are lossy and resonant, extraction of the €requency-dependent properties from TDR can be difficult.
The TDR measurement of the microstrip line is shown in Fig. 5. From this measurement, the characteristic impedances around DC are 50 ohms because the steady state level is almost same as the input level. The dip in Fig. 5 was caused by pamsitic capacitances in the pad transition. Since the tail is almost constant after the settling time, the line can be assumed to have real-value characteristic impedances based on the TDR s i m lations. 0.02 I
1
i\
st
Voltage(V)
0 -0.05 -0.15 -O.'
1 4
-0.25
I
-0'30
400
800 1200 1600 2000 2400 Timebs]
Fig. 7. TDR measurements of an inductor
-0.08 I 0
400
I
800
1200 Time[ ps]
Fig. 5. TDR measurement of a microstrip line
The extracted frequency-dependent characteristic impedance is plotted in Fig6 after de-embedding the pad transition. The characteristic impedance approaches the quasi-TEM approximation, 36 ohm, with frequency. Quasi-TEM methods give good correlation only at high frequencies where the current is confined to the surface of the conductor. From 7.5GHz, the characteristic impedance goes down steeply implying our lumped pad transition model is not good.
-0.8
1
- 1 ' . ' . " ' - 1 -0.8 -0.6-0.4 -0.2 0
"
Fig. 8. Sparameter (SI 1) ofthe inductor @C solid line :TDR
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"
0.2 0.4 0.6 0.8
J1
- 4.3GHz).dotted line : NA,
We have shown that this is possible using the 1-port calibmtion. Fig.7 shows the TDR measurements of an inductor with the other end shorted. The vertical axis is time and the horizontal axis is the voltage amplitude of the pulses. In Fig. 8, the extracted Sparameters from a Network Analyzer and TDR have been compared. The two results agree well with.each other. The inductor has a resonant frequency of 3.6 GHz, Q of 80 at 2GHz and inductance of lOnH [12]. Fig. 9 shows the quality factor of the inductor. The quality factor is fairly high from lGHz to 2.5GHz, whereby these inductors find application in consumer electronics.
I
160 Q 140-
-: TDR
120'
........... : NA
The VNA measures and displays the various combinations of incident and reflected waves, commonly known as S paramters [ 151. The impedance of a one-port DUT can be calculated from its voltage reflection coefficient (SI 1) by inverting the defining formula:
(4)
where & is the connecting impedance of the instruments, usually 50 ohms. A state-of-the-art VNA may have around one-tenth of a decibel repeatability and a fraction of a dB absolute error in SI1 measurements, which allows the accurate measurements of impedances not much smaller or greater than 50 ohms. With very low impedances, however, the inversion of (4) has to resolve two vectors of almost equal magnitude (full reflection), and the accuracy gradually breaks down.
100'
It was shown in [16] that the two-port self-impedance measurement setup can extend the capabilities of one-port vector network analyzer measurements by more than an order of magnitude, enabling the measurement of PDN impedances below a milliohm.
0.5
1
1.5 2
The equivalent circuit of PDN self and transfer impedance measurements is shown in Figure 11.
2.5 3 3.5 4 FreauencvlGHzl
Self impedance:
Fig. 9. Quality factor of the inductor
Coax and Portl of VNA: 50 ohm
111.PDN MEASUREMENTS WITH VNA
Coax and Port2 VNA: 50 ohm
Of
The Vector Network Analyzer (VNA), widely used in mcrowave and RF applications, can be helpful in making power-distribution measurements of low impedance values.
Transfer impedance: A . Instrumentation
Cable and Portl of VNA: 50 ohm
As shown in Figure 10, the VNA consists of a tunable sinusoidal source and tracking receiver. The receiver can be connected to measure the incident wave (al) or reflected wave ( b l ) to and from the device under test (DUT), or the transmitted wave (b2) through the DUT.
Cable and Port2 of VNA: 50 ohm
Figure 11. Equivalent circuit of VNA connections for DUT self-andtrans fer-impedance measurements.
I
Directional coupler
Portl and Port 2 of VNA: 25 ohm
Portl
DUT
I Port2 "-
Figure IO. Block schematic of vector network analyzer.
Figure 12. Simplified equivalent circuit.
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On Figure 11, b~and b2 represent the inductive discontinuities of the cable-DUT interface. By first neglecting these inductive discontinuities, the simplified equivalent circuit is shown in Figure 12.
Note that the effect of connecting discontinuities is greatly reduced by the two-port setup: the discontinuity is in series to the 50-ohm connecting impedance as opposed to the unknown (usually very low) DUT impedance. With a 0.4nH discontinuity inductance, the corner frequency of the error terms in (8) and (9) is around 20GHz.
The measured S-parameter values first are converted from the usual logarithmic dB scale to ratios by:
Assuming small DUT impedances (ZDUT
