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Laboratory #1: Network Analysis - Open, Short, and Matched Load
I. OBJECTIVES
The objective of this experiment is to become acquainted with the Agilent 8510C Network Analyzer. Demonstrate your ability to calibrate the network analyzer and measure:
- Impedance
- S-parameters
- VSWR Be able to use the Log-Mag, and Polar Plot options.
The results of the analyses are experimentally verified using a network analyzer. S11 and SWR
are found.
II. INTRODUCTION
One common method for measuring the reflection and transmission characteristics of any device under test (in this case open, short, and matched loads) involves the using a network analyzer. A network analyzer allows convenient measurements of signal reflection and transmission in a variety of formats. It can measure signal delay, phase, and gain of the device under test (DUT). All of these measurements are made with respect to the source and terminal impedance of the network analyzer. The default impedance of the HP8752A or equivalent network analyzer is set at 50 Ω.
The signal reflected from the DUT is usually measured as a ratio to the incident signal. It can be expressed as reflection coefficient or return loss. These measurements are described mathematically as,
Reflection coefficient ≡ = reflected power incident power
E
E
refl inc
= ρ (magnitude only)
= Γ (Reflection magnitude and phase) (9)
Return loss (dB) = −20 log ρ (10)
Standing Wave Ratio −Γ
SWR (pronounced " swir " as in swirl ) (11)
Displaying the reflection measurement in polar form on the network analyzer with a marker allows direct determination of the complex impedance of the DUT. The center of the circle represents a coefficient Γ of 0 (a perfect match, no reflected signal). The outermost circumference of the scale represents a |Γ| of 1 (100% reflection). The phase angle is directly read from the display. The magnitude and phase will be directly displayed in the marker data readout for any frequency.
The amount of power reflected from a device is directly related to the impedances of the DUT and the measurement instrument. Γ = 0 occurs when the DUT and the analyzer have identical impedances. A short circuit has Γ = 1 ∠ 180 °. Every other value of Γ corresponds uniquely to a complex device impedance. In terms of impedances,
Z Z
Z Z
DUT o DUT o
where Zo is the impedance of the measurement instrument,
ZDUT is the impedance of the DUT.
To facilitate computations, the normalized (in this case normalized to 50 Ω) impedance is,
Z
Z
N Z
DUT o
S-parameters are commonly used to characterize high frequency circuits. S-parameters (or Scattering-parameters) basically are two-port characteristics of the DUT. Additionally, insight into the behavior of traveling waves are readily deduced from S-parameters.
S-parameters can readily be found using the schematic of the test set-up shown in Figure 3.
DUT 2-Port Network Z^ L
E (^) i E (^) r1 E (^) r
E (^) i
Zo
Figure 3. Two Port Network Used For S-Parameter Measurements
Define new variables with respect the a characteristic impedance of the measurement instrument,
a
E
Z
i o
1 = 1 , a E Z
i o
2
b
E
Z
r o
1 = 1 , b E Z
r o
2
S-parameters relates these four waves as follows:
To change to the scale of a graph, on the RESPONSE menu, press SCALE, and turn the thumb knob until the graph looks like you want it to. Alternatively, choose a scale on the number pad (then press x1 on the number pad). To get a hard copy on the plotter:
- Put paper in the plotter/printer Turn on plotter (back left side).
- On AUXILLARY menu (bottom of Network analyzer panel), Press COPY, Plot to Printer, specify what to plot (ALL).
III. PROCEDURE
A. Find equations for the S-parameters for the following simple circuits: 1. a) Short b) Open c) Matched Load (S12 and S21 are meaningless)
B. READ the presentation on Network Analysis
C. Determine Γ and SWR for the loads provided
- Measure the Γ and SWR of the simple circuits provided from 10 MHz-3 GHz. Use the Log- Mag, and Polar Plot Options. Use markers at 49 MHz, 900 Hz and 2.4 GHz Compare to your expected values.
- Plot at least one of your plots on the plotter in Log-Mag format.
- Carefully save written instructions/notes on how to make these measurements (because you will be making them AGAIN).
- Summarize your results. How well do your results agree with expected results?
