Istvan NovakMeasuring milliohms and picohenrys 1
DesignCon, Feb. 2000
Measuring Milliohms and
PicoHenrys in Power Distribution
Networks
Istvan Novak
SUN Microsystems, Inc.
One Network Drive
Burlington, MA 01803
Istvan NovakMeasuring milliohms and picohenrys 2
DesignCon, Feb. 2000
Outline
• Introduction
• Two-port VNA impedance measurements
• Low-frequency limitations
• Enhancement with transformer or amplifier
• High-frequency limitations
• Enhancement with ferrite-covered cable
• Measured power-distribution networks
• Resources
• References
Istvan NovakMeasuring milliohms and picohenrys 3
DesignCon, Feb. 2000
Requirements in Power Distribution
0.1
1
10
100
1000
1992 1994 1996 1998 2000
Vdd [V]
Power [W]
Current [A]
Frequency[MHz]Ztarget [mohm]
Ltarget [nH]
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DesignCon, Feb. 2000
What is a VNA• Tuned sinewave generator
• Directional couplers
• Tracking receiver(s)
Source
Receiver
DUT
Directional coupler
b1 a1
b2
Port1
Port2
01
221
01
111
2
2
|
|
=
=
=
=
a
a
ab
S
ab
S
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DesignCon, Feb. 2000
Two-Port Self-Impedance Measurement
Cable and Port2 of VNA: 50 ohmZDUT
Cable and Port1 of VNA: 50 ohm
VS
• S21 instead of S11 is measured
• S21 uncertainty is less
• Zp is in series to 50 ohms instead of ZDUT
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DesignCon, Feb. 2000
Two-Port Self-Impedance Reading
First-order calculation:
Assume that
• Lp ~ 0
• ZDUT << Z0
ZDUT
Port1 and Port 2 of VNA: 25 ohm
VS
ZDUT = Z11 = S21* 25 [ohm]
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DesignCon, Feb. 2000
Transfer Impedance Measurement
Cable and Port2 of VNA: 50 ohm
DUT
Cable and Port1 of VNA: 50 ohm
VS V1 V2
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DesignCon, Feb. 2000
Transfer Impedance Reading
First-order calculation:
Assume that
• Lp ~ 0
• Z11 << Z0
• Z22 << Z0
• Z21 << Z0
Z21 = Z12 = S21* 25 [ohm]
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DesignCon, Feb. 2000
S21 Uncertainty• |S21| uncertainty of HP8720D:
<1dB in the |S21| > -60dB range
<3dB in the |S21| > -70dB range
• Impedance uncertainty:
1dB (10%) for ZDUT >
25milliohms
3dB (40%) for ZDUT > 8milliohms
Istvan NovakMeasuring milliohms and picohenrys 10
DesignCon, Feb. 2000
Equivalent Circuit of Probes Connection
Lp1 Lp2
Cable and Port2 of VNA: 50 ohmDUT
Cable and Port1 of VNA: 50 ohm
VS V1 V2
Lp1 Lp2
Coax and Port2 of VNA: 50 ohmZ11=ZDUT
Coax and Port1 of VNA: 50 ohm
VS
Self impedance:
Transfer impedance:
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DesignCon, Feb. 2000
S21 Conversion to Self Impedance
2121
2
2121
121 1
125
21
12 S
jS
ZZZ
S
ZSZ p
ii −+
∗∗≈+−
=ωτ
Where Z1 = 50+jωLp1
Z2 = 50+jωLp2
τp = Lp/50
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DesignCon, Feb. 2000
S21 Conversion to Transfer Impedance
+
+∗
∗+
+∗∗
≈+
+
+
=
2
22
1
112
21
21
2
12121
2
22
1
11
121
11
2501
125
21
11
2
ZZ
ZZ
S
jS
ZZZSZZ
ZZ
ZSZ
p
ji
ωτ
Where Z1 = 50+jωLp1
Z2 = 50+jωLp2
τp = Lp/50
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DesignCon, Feb. 2000
Low-Frequency Ground Loop
VNA Port2:50 ohm
ZDUT=0
VNA Port1:50 ohm
VS
Lb1 Lb2Rb1 Rb2
Lc1 Rc1 Rc2 Lc2
Imp. magnitude [ohm]
1.E-04
1.E-03
1.E-02
1.E-01
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Frequency [Hz]
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DesignCon, Feb. 2000
Ground-Loop DC Error
VNA Port2:50 ohm
ZDUT=0
VNA Port1:50 ohm
VS
Rb1 Rb2
Rc1 Rc2
21_ || bberrorDC RRR =
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DesignCon, Feb. 2000
Eliminating Ground Loop
Transformer
Differential amplifier
VNA Port2:50 ohm
ZDUT
VNA Port1:50 ohm
VS
Lb1 Lb2Rb1 Rb2
Lc1 Rc1 Rc2 Lc2
1:1
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DesignCon, Feb. 2000
Transformer
Phillips core: TX51/32/19-3F3
• Diameter: 52mm
• 2x50 turns
• AWG 20
• bifilar
• SMA female
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DesignCon, Feb. 2000
Transformer ImpedanceImpedance magnitude [dBohm]
5.0E+01
7.0E+01
9.0E+01
1.1E+02
1.E+04 1.E+05 1.E+06
Frequency [Hz]
• HP4395B
• HP87512A
• Open secondary
• Lmain=9.5mH
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DesignCon, Feb. 2000
Transformer Response (1)Through response [dB]
-1.4E+01
-1.2E+01
-1.0E+01
-8.0E+00
-6.0E+00
-4.0E+00
-2.0E+00
0.0E+00
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Frequency [Hz]
• 1:1 transformer
• HP4395B
• 50 ohms terminations
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DesignCon, Feb. 2000
Transformer Response (2)
S21 [dB]
-4.87E+01
-4.86E+01
-4.85E+01
-4.84E+01
-4.83E+01
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Frequency [Hz]
• 1:1 transformer
• HP4395B
• Calibrated with 50 ohms terminations
• 0.1 ohms shunt
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DesignCon, Feb. 2000
Calibration Setup
VNA Port2:50 ohm
Calibration withZDUT=0.1-ohm reference
VNA Port1:50 ohm
VS 1:1
Isolationtransformer
50-ohm coax 50-ohm coax
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DesignCon, Feb. 2000
Isolation Amplifier
250
4725
25
250
_
+
AD815
+7V
-7V
IN-
IN+
Out
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DesignCon, Feb. 2000
Reduced Error Floor by Increased P
S21 [dB]
1.98E+01
1.99E+01
2.00E+01
2.01E+01
2.02E+01
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08
Frequency [Hz]
• Calibration at –5dBm
• HP4395B
• Power changed to +15dBm
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DesignCon, Feb. 2000
Residual NoiseImpedance [ohm]
1.E-06
1.E-05
1.E-04
1.E-03
1.E+04 1.E+05 1.E+06
Frequency [Hz]
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DesignCon, Feb. 2000
Reading of Shorts
Imp. magnitude [ohm], wire-short, sheet-short
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+03 1.E+04 1.E+05 1.E+06
Frequency [Hz]
• Isolation transformer
• HP4395B
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DesignCon, Feb. 2000
Measuring Low ESRImpedance magnitude [ohm]
1.E-03
1.E-02
1.E-01
1.E+00
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06Frequency [Hz]
• 1:1 transformer
• HP4395B
• 0.1ohm calibration
• OSCON 1500uF 4V
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DesignCon, Feb. 2000
Voltage Regulator Module
• 1.5V VRM
• Output pins connected by copper planes
• SSMB connectors
Istvan NovakMeasuring milliohms and picohenrys 27
DesignCon, Feb. 2000
VRM Zout
Impedance magnitude [ohm] power off, power on
1.E-04
1.E-03
1.E-02
1.E-01
1.E+03 1.E+04 1.E+05 1.E+06Frequency [Hz]
• 1.5V VRM
• No external capacitor
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DesignCon, Feb. 2000
Limitations at High FrequenciesFinite braid surface transfer impedance
Braid resonancesResidual impedance [ohm]
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E+05 1.E+06 1.E+07 1.E+08 1.E+09Frequency [Hz]
Plain coax
Coax, 2x4 ferrites
Solution:
Absorption ferrites
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DesignCon, Feb. 2000
Ferrite-Covered Cable
Istvan NovakMeasuring milliohms and picohenrys 30
DesignCon, Feb. 2000
Reference: Connection to Solid Plane
d=70 mil center-to-center spacing
a=15-mil radius drilled viast=0.6-mil (half ounce)
copper plane
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DesignCon, Feb. 2000
Probes and Vias
• Test board with via locations
• SMA-SSMB adaptors
• Probe: SSMB jack with two pins
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DesignCon, Feb. 2000
Reading Across Solid Plane
Impedance magnitude [ohm]
1.E-04
1.E-03
1.E-02
1.E-01
1.E+05 1.E+06 1.E+07 1.E+08 1.E+09Frequency [Hz]
• Half-ounce Cu
• 30-mil vias
• 70-mil via spacing
• 0.52 milliohms
• 5.5pH
Istvan NovakMeasuring milliohms and picohenrys 33
DesignCon, Feb. 2000
DC Resistance Across Solid Plane
t: thickness
d: separation
a: radii
A B
+
+
+
+
+≈
12
1
12
1ln1
12
2
ta
td
ta
aRAB πσ
Istvan NovakMeasuring milliohms and picohenrys 34
DesignCon, Feb. 2000
Combined Impedance of PDN
• VRM
• 2x3”x4” 2-mil planes
• Bulk capacitors
• 90 bypass capacitors
Impedance magnitude [ohm]
1.E-04
1.E-03
1.E-02
1.E-01
1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08
Frequency [Hz]
Istvan NovakMeasuring milliohms and picohenrys 35
DesignCon, Feb. 2000
Simulated PDN Impedance
Impedance of parallel capacitor banks
1.E-04
1.E-03
1.E-02
1.E-01
1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02
Frequency [MHz]
ZcSum
Z_corr
Istvan NovakMeasuring milliohms and picohenrys 36
DesignCon, Feb. 2000
Recommended Resources
Hewlett Packard Vector Network Analyzers:
• HP 4395 VNA 10Hz-500MHz
• HP 4396 VNA 100kHz-1.8GHz
• HP87512A DC-2GHz Transmission/Reflection Test Set
• HP 8720D VNA 50MHz-20GHz
Circuit simulator software:
• Avant! HSPICE
Istvan NovakMeasuring milliohms and picohenrys 37
DesignCon, Feb. 2000
Conclusions
• Two-port measurements reduce effect of
discontinuities
• Limitation at low frequencies: cable-braid ground loop
• Ground-loop is eliminated by transformer or amplifier
• Limitation at high frequencies: braid leakage and
resonance
• Reliable reading and good correlation to simulations is
achieved in the sub-milliohm range