Grundlagen der Impedanzmessung presented by Michael Benzinger Application Engineer - RF & MW
Agenda Impedance Measurement Basics Impedance Basics Impedance Dependency Factors Impedance Measurement Methods / Instruments
Michael Benzinger Application Engineer - RF & MW Grundlagen der Impedanzmessung Teil 1: Impedance Basics
Impedance Definition Z(f): Total opposition a device or circuit offers to the flow of AC Imaginary axis Z = R + jx = Z θ +j X Z (R, X) R = Z cos θ X = Z sin θ Z Z = R 2 + X 2 θ = tan -1 (X/R) θ R Real axis Unit of impedance: ohm (Ω)
Impedance Plane Inductor L X L = 2πfL = ωl Capacitor C 1 1 X C = = 2πfc ωc R jx L R -jx C jx L δ θ R (a) Inductive vector represented on impedance plane Z -jx C δ θ (b) Capacitive vector represented on impedance plane R Z
Admittance Plane G G -jb L δ θ -jb L G (c) Inductive vector represented on admittance plane Y jb C δ θ jb C (d) Capacitive vector represented on admittance plane Y G
Series and parallel combinations Real and imaginary components are connected in series. Real and imaginary components are connected in parallel. R jx R jx G Z = R + jx (Impedance is better to express.) jrx RX 2 R 2 X Z = = + j R + jx R 2 + X 2 R 2 + X 2 (Impedance makes it a bit complex.) Y = G + jb (Admittance is better to use.) jb
Quality and Dissipation Factors Q = Energy stored Energy lost = X L R (inductors) As R 0, Q (better component) D = 1 Q = R -X C (capacitors) As R 0, D 0 (better component)
Michael Benzinger Application Engineer - RF & MW Impedance Analysis Teil 2: Impedance Dependency Factors
Measurement Discrepancy Q = 165 Q = 120 Z Analyzer LCR meter L = 5.231nH L = 5.310 uh LCR meter Z Analyzer
Measurement Discrepancy Reasons True, Effective and Indicated Values Circuit Model (Translation Equations) Component Dependency Factors Measurement Errors Measurement Uncertainty
Parasitics: there is no pure R, C, or L Complicate the Measurements No real components are purely resistive or reactive Every component is a combination of R, C and L elements The unwanted elements are called parasitics Intrinsic C Unwanted R and L of leads Unwanted R and C of dielectric Capacitor Equivalent Circuit
Parasitics: there is no pure R, C, or L Capacitor Equivalent Circuit Capacitor Model Rs, Ls, Rp, Cp? Series Model Rs Cs Rp Parallel Model Low-Impedance Device (Large C, Small L; Z < 10 Ω) Cp High-Impedance Device (Small C, Large L; Z > 10 kω)
Parasitics: there is no pure R, C, or L Which Model Is Correct? Rp Rs Cs Series model Cp Parallel model Both are correct Cs = Cp (1 + D 2 ) One is a better approximation For high Q or low D components, C S C P
Parasitics: there is no pure R, C, or L What do instruments measure, calculate or approximate? Vector Voltmeter Method I-V Probe Method Reflection Coefficient Method Measured Direct Calculations I, V I, V V Z = I Z = R+jX, θ = ATAN(X/R) Y = 1/Z, Y = G +j B x,y Z = Z o 1 + 1 - Model-based Approximations Ls, Lp, Cs, Cp, Rs or ESR, Rp, D, Q D U T? Rs Cs Rp Cp
Ideal, Real, and Measured values Which value do we measure? IDEAL REAL MEASURED ± % Instrument Test fixture Real-world device
Component Dependency Factors Measurement conditions that determine the measured impedance value Effects depend on component materials and manufacturing processes Four major factors: Test signal frequency Test signal level DC voltage and current bias Environment (temperature, humidity, etc.)
Component Dependency Factors Reactance vs. Frequency Capacitor X X C = 1 ωc X L = ωl Frequency ω
Component Dependency Factors Example Capacitor Resonance Impedance vs. Frequency ωl 1 ωc Z θ f s
Measurement Error Measurement Setup Instrument Port Extension Test Fixture DUT R x+ jxx
Measurement Error Sources of Measurement Errors Technique Complex Inaccuracies Residuals Residuals Noise Parasitics Instrument Port Extension Test Fixture DUT R x+ jxx
Measurement Error Actions for limiting measurement errors Technique Complex Inaccuracies Residuals Residuals Noise Parasitics Instrument Port Extension Test Fixture DUT R x+ jxx Guarding Calibration LOAD Compensation Compensation Shielding
Michael Benzinger Application Engineer - RF & MW Impedance Analysis Section 3: Impedance Measurement Methods
Measurement Methods Types of Measurement Methods (a) Auto-Balancing Bridge (b) RF I-V (c) Network Analysis (Reflection Coefficient) Others Bridge Resonant (Q-adapter/Q-meter) I-V (Probe)
Measurement Method Selection Criteria 1) Frequency 2) DUT impedance 3) Required measurement accuracy These determine the most suitable method 4) Electrical test conditions 5) Measurement parameters 6) Physical characteristics of DUT These determine the proper instrument and test fixture
Measurement Methods Comparison Impedance (Ω) 100M 10M 1M 100K 10K 1K 100 10 1 Auto-Balancing Bridge RF I-V Network/Reflection 10% of the measurement accuracy range for each method 100m 10m 1m 1 10 100 1K 10K 100K 1M 10M 100M 1G 10G Frequency (Hz)
Measurement Methods (a) Auto-Balancing Bridge Method Theory of Operation Virtual ground H DUT L R r V 1 I I = I r - I r + V 2 = -I r R r V2 Z = V 1 I r = -V 1 R r V 2
Auto-Balancing Bridge Terminal Configuration Two-terminal (2T) method Lc Lp Hp Hc L H DUT 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M Typical Impedance Measurement Range (Ω)
Auto-Balancing Bridge Terminal Configuration Three-terminal (3T) method G L H DUT 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M Typical Impedance Measurement Range (Ω)
Auto-Balancing Bridge Terminal Configuration Four-terminal (Kelvin, 4T) method Lc Lp Hp Hc DUT 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M Typical Impedance Measurement Range (Ω)
Auto-Balancing Bridge Terminal Configuration Five-terminal (5T) method G L c L p H p H c DUT 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M Typical Impedance Measurement Range (Ω)
Auto-Balancing Bridge Terminal Configuration Mutual inductance error For mω DUT L c L p H p H c M_ 2 V MEA M _ 2 I AC V DUT I AC DUT V MEA V DUT
Auto-Balancing Bridge Terminal Configuration Four-terminal pair (4TP) method Active Guard L c L p H p H c i i i i DUT i center = i shield 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M Typical Impedance Measurement Range (Ω)
Measurement Methods (b) RF I-V Method Theory of Operation Current Detection R V i Voltage Detection V v R/2 R V I DUT Z x Impedance Test Head V R V Z v x = = ( - 1) I 2 V i
Terminal Configuration in the RF Range H L A V Ro Go Co Lo DUT DUT (a) Connection Diagram (b) Schematic Diagram 1m 10m 100m 1 10 100 1K 10K 100K 1M 10M (c) Typical Impedance Measurement Range (Ω)
RF Test Fixtures Agilent-supplied test fixtures Cap Electrode DUT DUT Insulator Center Electrode DUT Outer Conductor To Test Port 7mm connector To Test Port (b) Coaxial Test Fixture (a) Non-coaxial Test Fixture
Measurement Methods (c) Network Analysis Method Theory of Operation V INC V V V r Reflected signal V r Z X - Z 0 Γ = = V ZX + Z INC 0 V INC OSC Directional bridge or coupler Incident signal Z X V r DUT
Which Measurement Method is the best? All are good. Each has advantages and disadvantages. Multiple techniques may be required.
Measurement Methods Summary Impedance (Ω) Auto-Balancing Bridge RF I-V Network/Reflection Frequency (Hz) Method Frequency Range Impedance Range Terminal Connections # of Ports Auto- Balancing Bridge 20 f 110 MHz 1 mω Z 100 MΩ (10% acc) 4-Terminal Pair, BNC 1 RF I-V 1 MHz f 3 GHz 0.2 Z 20 kω (10% acc) 7 mm 1 Network Analysis f 300 khz Z Z 0 7 mm, N-Type N 1
Measurement Methods and Agilent Products Measurement Method Agilent Product Frequency Range Auto-Balancing Bridge RF I-V Network Analysis (Reflection Coefficient) Network Analysis (Transmission Coefficient) 4263B LCR Meter E4980A Precision LCR Meter 4285A Precision LCR Meter 4294A Precision Impedance Analyzer 4291B Impedance/Material Analyzer 4287A RF LCR Meter E4991A Impedance/Material Analyzer PNA Series Vector Network Analyzers ENA Series Vector Network Analyzers ENA-LF Series Vector Network Analyzers 100 Hz to 100 khz spot 20 Hz to 2 MHz 75 khz to 30 MHz 40 Hz to 110 MHz 1 MHz to 1.8 GHz 1 MHz to 3 GHz 1 MHz to 3 GHz 300 khz to 1,05 THz 9 khz to 20 GHz 5 Hz to 3 GHz
Combined Network Impedance Analyzer Impedance analysis function for the E5061B Z θ NA + ZA in one box Fully supports traditional ZA functions Migrate legacy combo analyzers (4195A, 4395/96x, 4194A, 4192A)
Overview E5061B-3L5 LF-RF NA option Low Frequency (5 Hz~) Wide dynamic range at LF Features for LF applications (1 Mohm inputs, probe power, DC bias source, etc) 10.4 inch LCD touch screen Probe power (Option 3L5 only) USB Zin = 1 MΩ / 50 Ω ATT = 20 db / 0 db Gain-phase test port (Option 3L5 only) - LF OUT (source) - R (1 MΩ/50 Ω) - T (1 MΩ/50 Ω) S-parameter test port (Option 2x5/ 2x7/3L5), or Transmission/Reflection test port (Option 1x5/1x7) T R Handler I/O GPIB USBTMC Peripheral ports (USB, LAN, XGA output) ATT ATT R1 R2 Zin Zin T1 T2 T R LF OUT Port-1 Port-2 Gain-phase test port (5 Hz to 30 MHz) S-parameter test port (5 Hz to 3 GHz, 50 Ω ) High stability freq. reference (Option 1E5) External trigger-in/out
Key features - Covers moderate Z range S-Parameter (5 Hz - 3 GHz) Test port Gain-Phase (5 Hz - 30 MHz) Applicable Z-range Low-Z Mid-Z High-Z 1 mω ~ 1 Ω 1 kω ~ 100 kω Reflection Port 1 Refl / Port 2 Refl S1 1 Mid 7-mm type fixtures Configuration Series Port 1-2 Series S2 1 GP Series (T 50Ω, R 1MΩ) 1MΩ input TR Mid - High 4-Terminal Pair type fixtures Shunt Port 1-2 Shunt S21 GP Shunt (T 50Ω, R 50Ω) Power splitter TR Low - Mid Shunt Series User fixtures are required
Key features - Migrate legacy combo analyzer 7 mm and 4-terminal pair (4TP) test fixtures can be utilized 7 mm test fixture with 16201A Reflection method (S-Parameter, Port 1) 5 Hz to 3 GHz 16092A 16201A 4-terminal pair test fixture Series-thru method (Gain-Phase, T 50Ω, R 1MΩ) 5 Hz to 30 MHz 16047E
10% measurement accuracy range (E5061B, S-Parameter test port) 1,E+05 100 kω 1,E+04 10 kω 1,E+03 1 kω E5061B (SPD) S-Parameter, Series-thru E5061B (SPD) S-Parameter, Reflection Impedance [Ohm] 1,E+02 100 Ω 1,E+01 10 Ω 1,E+00 1 Ω 100 1,E-01 mω 10 mω 1,E-02 1 mω 1,E-03 E5061B (SPD) S-Parameter, Shunt-thru 7 mm test fixture 1,E-04 100 100 100 1,E+00 1,E+01 10 Hz 1,E+02 1,E+03 1 khz 1,E+04 10 khz Hz 1,E+05 1,E+06 1 MHz 10 1,E+07 MHz khz 1,E+08 MHz 1,E+09 1 GHz 1,E+10 Frequency [Hz] Definitions - Specification (Spec): Warranted performance. Specifications include guardbands to account for the expected statistical performance distribution, measurement uncertainties, and changes in performance due to environmental conditions. - Supplemental performance data (SPD): Represents the value of a parameter that is most likely to occur; the expected mean or average. It is not guaranteed by the product warranty. For more details about conditions for defining accuracy, please refer to the Data Sheet.
10% measurement accuracy range (E5061B, Gain-Phase test port) 1,E+05 100 kω 1,E+04 10 kω 1,E+03 1 kω E5061B (SPD) Gain-Phase, Series-thru Impedance [Ohm] 1,E+02 100 Ω 1,E+01 10 Ω 1,E+00 1 Ω 100 1,E-01 mω 4-terminal pair test fixture 10 mω 1,E-02 1 mω 1,E-03 E5061B (SPD) Gain-Phase, Shunt-thru 1,E-04 100 100 100 1,E+00 1,E+01 10 Hz 1,E+02 1,E+03 1 khz 1,E+04 10 khz Hz 1,E+05 1,E+06 1 MHz 10 1,E+07 MHz khz 1,E+08 MHz 1,E+09 1 GHz 1,E+10 Frequency [Hz] Definitions - Specification (Spec): Warranted performance. Specifications include guardbands to account for the expected statistical performance distribution, measurement uncertainties, and changes in performance due to environmental conditions. - Supplemental performance data (SPD): Represents the value of a parameter that is most likely to occur; the expected mean or average. It is not guaranteed by the product warranty. For more details about conditions for defining accuracy, please refer to the Data Sheet.