1. Smith Chart

2. Rectilinear impedance plane
Smith Chart Review +R
+jX
-jX . 90 o
Polar plane
1.0 .8 .6 .4
180 o + - .2 o
Rectilinear impedance plane
-90 o
Constant X
Z = Zo L
Constant R G =
Smith Chart maps rectilinear impedance plane onto polar plane
The amount of reflection that occurs when characterizing a device depends on the impedance the incident signal sees. Let's review how complex reflection and impedance values are displayed. Since any impedance can be represented as a real and imaginary part (R+jX or G+jB), we can easily see how these quantities can be plotted on a rectilinear grid known as the complex impedance plane. Unfortunately, the open circuit (quite a common impedance value) appears at infinity on the x-axis.
The polar plot is very useful since the entire impedance plane is covered. But instead of actually plotting impedance, we display the reflection coefficient in vector form. The magnitude of the vector is the distance from the center of the display, and phase is displayed as the angle of vector referenced to a flat line from the center to the rightmost edge. The drawback of polar plots is that impedance values cannot be read directly from the display.
Since there is a one-to-one correspondence between complex impedance and reflection coefficient, we can map the positive real half of the complex impedance plane onto the polar display. The result is the Smith chart. All values of reactance and all positive values of resistance from 0 to ¥ fall within the outer circle of the Smith chart. Loci of constant resistance now appear as circles, and loci of constant reactance appear as arcs. Impedances on the Smith chart are always normalized to the characteristic impedance of the test system (Zo, which is usually 50 or 75 ohms). A perfect termination (Zo) appears in the center of the chart.
Z = 0
(short)
Z =
(open) L L G G = 1
±180 O = 1 O
Smith Chart

3. Circuits components

4. Smith Chart main points

5. From S parameters to impedance

6. IF BW and averaging Heterodyne detection scheme IF BW reduction
Dynamic Range (definition)

7. Smoothing trace
Smoothing (similar to video filtering) averages the formatted active channel data over a portion of the displayed trace. Smoothing computes each displayed data point based on one sweep only, using a moving average of several adjacent data points for the current sweep. The smoothing aperture is a percent of the swept stimulus span, up to a maximum of 20%.
Rather than lowering the noise floor, smoothing finds the mid-value of the data. Use it to reduce relatively small peak-to-peak noise values on broadband measured data. Use a sufficiently high number of display points to avoid misleading results. Do not use smoothing for measurements of high resonance devices or other devices with wide trace variations, as it will introduce errors into the measurement.

8. Averaging trace
Averaging computes each data point based on an exponential average of consecutive sweeps weighted by a user-specified averaging factor. Each new sweep is averaged into the trace until the total number of sweeps is equal to the averaging factor, for a fully averaged trace. Each point on the trace is the vector sum of the current trace data and the data from the previous sweep. A high averaging factor gives the best signal-to-noise ratio, but slows the trace update time. Doubling the averaging factor reduces the noise by 3 dB.

9. IF BW reduction
IF bandwidth reduction lowers the noise floor by digitally reducing the receiver input bandwidth. It works in all ratio and non-ratio modes. It has an advantage over averaging as it reliably filters out unwanted responses such as spurs, odd harmonics, higher frequency spectral noise, and line-related noise. Sweep-to-sweep averaging, however, is better at filtering out very low frequency noise. A tenfold reduction in IF bandwidth lowers the measurement noise floor by about 10 dB. Bandwidths less than 300 Hz provide better harmonic rejection than higher bandwidths.

10. Impedance Measurements

11. Which Value Do We Measure?
TRUE
EFFECTIVE
Before proceeding to practical measurements, we need to understand the concept of True, Effective and Indicated values. This is essential since we all tend to forget that the instrument does NOT necessarily measure what we want to measure. By the way, which value do instruments measure?
The TRUE value excludes all parasitics and is given by a math relationship involving the component's physical composition. If you think of a 50 Ohm PC board stripline, it is built up assuming that the dielectric constant K is constant. But in the real world this is not true. The TRUE value has only academic interest.
The EFFECTIVE value is what we generally want to measure because it takes into consideration the parasitics and dependency factors, as this figure shows. When designing and simulating circuits, only EFFECTIVE values should be used to reflect the actual circuit behavior. But the INDICATED value given by the instrument takes into account not only the real world device, but also the test fixture and accessories as well as the instrument inaccuracies and losses. What is the difference between TRUE and EFFECTIVE values? The quality of the component. And what is the difference between EFFECTIVE and INDICATED values? The quality of the instrument and above all the quality of the MEASUREMENT. Our goal is to make the INDICATED value as close as possible to the EFFECTIVE value
INDICATED %
+/-
Instrument
Test fixture
Real world device
Kobe Instrument Division
Back to Basics - LCRZ Module

12. Frequency vs. Measurement Techniques
Network Analysis
100KHz
RF I-V
1 MHz
1.8 GHz
I-V
10KHz
110MHz
Resonant
22KHz
30MHz
70MHz
Auto Balancing Bridge
This chart will help you visualize the frequency range for 5 measurement techniques. The frequency range numbers are a mix of practical and theoretical limits and should be used as a reference only. The autobalancing bridge basic accuracy is 0.05% while the network analysis one is 1.5%. This already uncovers possible trade-offs.
5HZ
40MHz 1 10
100 1K
10K
100K 1M
10M
100M 1G
10G
Frequency (Hz)
Kobe Instrument Division
Back to Basics - LCRZ Module

13. Auto Balancing Bridge Theory of Operation Virtual ground H R L 2 DUT I
I = I 1 2 - +
V = I R 2 2 V 2 2 V
V R 1 1 2
Z = = I 2 V 2
Kobe Instrument Division
Back to Basics - LCRZ Module

14. Advantages and Disadvantages
Auto Balancing Bridge
Advantages and Disadvantages
Most accurate, basic accuracy 0.05%
Widest measurement range
C,L,D,Q,R,X,G,B,Z,Y,O,...
Widest range of electrical test conditions
Simple-to-use
Let us summarize the advantages and disadvantages of each of the measurement techniques.
The Autobalancing bridge technique is by far the best technique for measurements below 40 MHz. It provides the most accurate measurements possible and has the widest impedance measurement range. Both of these are critical for accurate component analysis. A wide range of AC and DC stimulus can be applied to the component. In addition, because this is a low frequency technique, it is the simplest measurement technique to use.
Low frequency, f < 40MHz

15. Resonance (Q - Meter) Technique
Theory of Operation
Tune C so the circuit resonates
At resonance X = -X , only R remains D C D
DUT
L (X ), R D D e Z
Tuning C
(X c) ~ e I= V V
OSC
X = = (at resonance) C V I
R V e D
|X | R D
|X |
|V| e C
Q = = = R D
Kobe Instrument Division
Back to Basics - LCRZ Module

16. Advantages and Disadvantages
Resonant Method
Advantages and Disadvantages
Very good for high Q - low D measurements
Requires reference coil for capacitors
Limited L,C values accuracy
Vector
Scalar
75kHz - 30MHz
22kHz - 70MHz
automatic and fast
manual and slow
easy to use
requires experienced user
The Resonant technique, or Q-meter, used to be a very manual measurement technique. However, the design of automatically tunable air capacitor standards allows today fast and error free measurement of high Q or low D components. In low D capacitor test, it is still difficult to achieve high accuracy measurements due to the need for very stable reference inductors, which are difficult to design.
Testing chip or SMD capacitors requires specific test fixtures which have strays, essentially stray capacitance, that influence the value of the tuning capacitance. With the new automatic technique, test fixture parasitics can be compensated for by offset compensation. This requires accurate design and evaluation of the stray capacitance of the test fixture.
No compensation
limited compensation

17. I - V Probe Technique Theory of Operation R V 2 V = I R V V V R I Z =1 V
V R I 1 1 2 2
Z = = I V
DUT 2 2
Kobe Instrument Division
Back to Basics - LCRZ Module

18. Advantages and Disadvantages
I-V (Probe)
Advantages and Disadvantages
Medium frequency, 10kHz < f < 110MHz
Moderate accuracy and measurement range
Grounded and in-circuit measurements
Simple-to-use
The I-V, or "probe technique", provides very good mid-frequency range performance, extending up to 100 MHz. Another key feature of this technique is that it is a floating measurement technique, thus grounded and in-circuit measurements are very easy.

19. RF I-V Theory of Operation Low Impedance Test Head
High Impedance Test Head
Low Impedance Test Head
Current
Voltage
Current
Detection
Detection Vi
Detection
Voltage Vi
Detection Ro Ro Vv Ro
DUT Vv Ro
DUT
Kobe Instrument Division
Back to Basics - LCRZ Module

20. Advantages and Disadvantages
RF I-V
Advantages and Disadvantages
High frequency, 1MHz < f < 1.8GHz
Most accurate method at > 100 MHz
Grounded device measurement
The RF I-V technique provides very good high-frequency range performance, extending up to 1.8 GHz. This is the most accurate technique at frequencies higher than 100 MHz.
Although this is a 50 Ohm system, the technique has a very good impedance measurement range with quite good accuracy

21. Network Analysis (Reflection) Technique
Theory of Operation V
INC
DUT V R V
Z - Z R L O = = V
Z + Z
INC L O
Kobe Instrument Division
Back to Basics - LCRZ Module

22. Advantages and Disadvantages
Network Analysis
Advantages and Disadvantages
High frequency
- Suitable, f > 100 kHz
- Best, f > 1.8 GHz
Moderate accuracy
Limited impedance measurement range
(DUT should be around 50 ohms)
Network analysis is the best solution for very high frequency measurements, extending up to tens of GHz. Measurements as low as 100 KHz are possible with this technique (directional bridge low-end limit). Given the existence of the autobalancing bridge, I-V probe, and RF I-V techniques, it is advised that the network analysis technique be used for measurements above 1.8 GHz. Above 1.8 GHz, the reflection technique is the only measurement technique currently available.

23. TDR Theory of Operation Oscilloscope V V DUT Z Step Generator H V
INC R Z L
Series R & L
Parallel R & C t
Step Generator V
INC R
Z - Z L O
Z + Z =
Kobe Instrument Division
Back to Basics - LCRZ Module

24. Advantages and Disadvantages
TDNA (TDR)
Advantages and Disadvantages
Reflection and transmission measurements
Single and multiple discontinuities or impedance
mismatches ("Inside" look at devices)
DUT impedance should be around 50 ohms
Not accurate for m or M DUTs
or with multiple reflections
Although this is a 50 Ohm system, the technique has a very good impedance measurement range with quite good accuracy.
Good for test fixture design, transmission lines,
high frequency evaluations

25. Measurement examples

26. 1 nF
1 mH
10 nF
10 mH
1 kOhm
Corto circuito

27. 1 nF
1 mH
10 nF
10 mH
1 kOhm
Corto circuito

28. RF Device Characterization

29. Group delay

30. Use electrical delay to remove linear portion of phase response
Deviation from Linear Phase
Use electrical delay to remove linear portion of phase response
Linear electrical length added
Deviation from linear phase
RF filter response
Phase 45 /Div o
(Electrical delay function)
Phase 1 /Div o +
yields
Frequency
Frequency
Frequency
Looking at insertion phase directly is usually not very useful. This is because the phase has a negative slope with respect to frequency due to the electrical length of the device (the longer the device, the greater the slope). Since it is only the deviation from linear phase which causes distortion, it is desirable to remove the linear portion of the phase response. This can be accomplished by using the electrical delay feature of the network analyzer to cancel the electrical length of the DUT. This results in a high-resolution display of phase distortion (deviation from linear phase).
Low resolution
High resolution

31. What is group delay? f w f w p w Dw f Df = = * f -d f Group Delay (t )
Frequency g
Group Dw
Delay t f o
Phase
Average Delay Df
Group Delay (t )
-d f
d w = g
Frequency
d f d f -1
Deviation from constant group delay indicates distortion = *
360 o
Another useful measure of phase distortion is group delay. Group delay is a measure of the transit time of a signal through the device under test, versus frequency. Group delay is calculated by differentiating the insertion-phase response of the DUT versus frequency. Another way to say this is that group delay is a measure of the slope of the transmission phase response. The linear portion of the phase response is converted to a constant value (representing the average signal-transit time) and deviations from linear phase are transformed into deviations from constant group delay. The variations in group delay cause signal distortion, just as deviations from linear phase cause distortion. Group delay is just another way to look at linear phase distortion. f
in radians
Average delay indicates transit time w
in radians/sec f
in degrees
in Hz 2 = ( ) f w p f

32. Why measure group delay?
Phase
Phase f f
-d f
d w
-d f
d w
Group Delay
Group Delay
Why are both deviation from linear phase and group delay commonly measured? Depending on the device, both may be important. Specifying a maximum peak- to-peak value of phase ripple is not sufficient to completely characterize a device since the slope of the phase ripple is dependent on the number of ripples which occur per unit of frequency. Group delay takes this into account since it is the differentiated phase response. Group delay is often a more accurate indication of phase distortion. The plot above shows that the same value of peak-to-peak phase ripple can result in substantially different group delay responses. The response on the right with the larger group-delay variation would cause more signal distortion. f f
Same p-p phase ripple can result in different group delay