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•
Cancel discards the current selection and closes the keyboard. The input field of the calling
dialog is left unchanged.
The on-screen keyboard allows you to enter characters, in particular letters, without an external
keyboard; see Data Entry. To enter numbers and units, you can also use the DATA ENTRY keys on the
front panel of the instrument.
Step Size
A step
symbol next to a numeric input field opens the Step Size dialog to define an increment for
data variation using the Cursor Up/Down
buttons in the dialogs or the rotary knob.
•
The input value for the step size takes effect immediately; see Immediate vs. Confirmed
Settings.
•
Auto activates the default step size for the current input parameter.
•
Close closes the Step Size dialog.
Numeric Entry Bar
Single numeric values can be entered using the input field of the numeric entry bar. The numeric entry
bar appears just below the menu bar as soon as a function implying a single numeric entry is activated.
In contrast to dialogs, it does not hide any of the display elements in the diagram area.
The numeric entry bar contains the name of the calling function, a numeric input field including the
Cursor Up/Down
buttons for data variation and a step symbol
, and a Close button. Besides it is
closed automatically as soon as an active display element in the diagram area is clicked or a new menu
command is activated.
Display Formats and Diagram Types
A display format defines how the set of (complex) measurement points is converted and displayed in a
diagram. The display formats in the Trace – Format menu use the following basic diagram types:
•
Cartesian (rectangular) diagrams are used for all display formats involving a conversion of the
measurement data into a real (scalar) quantity, i.e. for dB Mag, Phase, Delay, SWR, Lin Mag,
Real, Imag and Unwrapped Phase.
•
Polar diagrams are used for the display format Polar and show a complex quantity as a vector
in a single trace.
•
Smith charts are used for the display format Smith and show a vector like polar diagrams but
with grid lines of constant real and imaginary part of the impedance.
•
Inverted Smith charts are used for the display format Inverted Smith and show a vector like
polar diagrams but with grid lines of constant real and imaginary part of the admittance.
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The analyzer allows arbitrary combinations of display formats and measured quantities (Trace –
Measure). Nevertheless, in order to extract useful information from the data, it is important to
select a display format which is appropriate to the analysis of a particular measured quantity;
see Measured Quantities and Display Formats.
Cartesian Diagrams
Cartesian diagrams are rectangular diagrams used to display a scalar quantity as a function of the
stimulus variable (frequency / power / time).
•
The stimulus variable appears on the horizontal axis (x-axis), scaled linearly (sweep types Lin
Frequency, Power, Time, CW Mode) or logarithmically (sweep type Log Frequency).
•
The measured data (response values) appears on the vertical axis (y-axis). The scale of the
y-axis is linear with equidistant grid lines although the y-axis values may be obtained from the
measured data by non-linear conversions.
The following examples show the same trace in Cartesian diagrams with linear and logarithmic x-axis
scaling.
Conversion of Complex into Real Quantities
The results to be selected in the Trace – Measure menu can be divided into two groups:
•
S-Parameters, Ratios, Wave Quantities, Impedances, Admittances, Z-Parameters and
Y-Parameters are complex.
•
Stability Factors and DC Input values (voltages, PAE) are real.
The following table shows how the response values in the different Cartesian diagrams are calculated
from the complex measurement values z = x + jy (where x, y, z are functions of the sweep variable).
The formulas also hold for real results, which are treated as complex values with zero imaginary part
(y = 0).
Trace Format
Description
Formula
dB Mag
Magnitude of z in dB
|z| = sqrt ( x
2
+ y
2
)
dB Mag(z) = 20 * log|z| dB
Lin Mag
Magnitude of z, unconverted
|z| = sqrt ( x
2
+ y
2
)
Phase
Phase of z
φ
(z) = arctan (y/x)
Real
Real part of z
Re(z) = x
Imag
Imaginary part of z
Im(z) = y
SWR
(Voltage) Standing Wave Ratio
SWR = (1 + |z|) / (1 – |z|)
Delay
Group delay, neg. derivative of the phase response
– d
φ
(z) / d
ω
(
ω
= 2
π
* f)
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An extended range of formats and conversion formulas is available for markers. To convert any
point on a trace, create a marker and select the appropriate marker format. Marker and trace formats
can be selected independently.
Polar Diagrams
Polar diagrams show the measured data (response values) in the complex plane with a horizontal real
axis and a vertical imaginary axis. The grid lines correspond to points of equal magnitude and phase.
•
The magnitude of the response values corresponds to their distance from the center. Values
with the same magnitude are located on circles.
•
The phase of the response values is given by the angle from the positive horizontal axis.
Values with the same phase on straight lines originating at the center.
The following example shows a polar diagram with a marker used to display a pair of stimulus and
response values.
Example: Reflection coefficients in polar diagrams
If the measured quantity is a complex reflection coefficient (S
11
, S
22
etc.), then the center of the polar
diagram corresponds to a perfect load Z
0
at the input test port of the DUT (no reflection, matched input),
whereas the outer circumference (|S
ii
| = 1) represents a totally reflected signal.
0
0
180
0
90
0
-90
0
Circles of equal
magnitude
Radial lines of
equal phase angle
Voltage reflection:
Open-circuited
load (Z = infinity)
Voltage reflection:
Short-circuited
load (Z = 0)
Matching
impedance (Z = Z
0
)
Examples for definite magnitudes and phase angles:
•
The magnitude of the reflection coefficient of an open circuit (Z = infinity, I = 0) is one, its phase
is zero.
•
The magnitude of the reflection coefficient of a short circuit (Z = 0, U = 0) is one, its phase is
–180
0
.
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Smith Chart
The Smith chart is a circular diagram that maps the complex reflection coefficients S
ii
to normalized
impedance values. In contrast to the polar diagram, the scaling of the diagram is not linear. The grid
lines correspond to points of constant resistance and reactance.
•
Points with the same resistance are located on circles.
•
Points with the same reactance produce arcs.
The following example shows a Smith chart with a marker used to display the stimulus value, the
complex impedance Z = R + j X and the equivalent inductance L (see marker format description in the
help system).
A comparison of the Smith chart, the inverted Smith chart and the polar diagram reveals many
similarities between the two representations. In fact the shape of a trace does not change at all if the
display format is switched from Polar to Smith or Inverted Smith – the analyzer simply replaces the
underlying grid and the default marker format.
Smith chart construction
In a Smith chart, the impedance plane is reshaped so that the area with positive resistance is mapped
into a unit circle.
The basic properties of the Smith chart follow from this construction:
•
The central horizontal axis corresponds to zero reactance (real impedance). The center of the
diagram represents Z/Z
0
= 1 which is the reference impedance of the system (zero reflection).
At the left and right intersection points between the horizontal axis and the outer circle, the
impedance is zero (short) and infinity (open).
•
The outer circle corresponds to zero resistance (purely imaginary impedance). Points outside
the outer circle indicate an active component.
•
The upper and lower half of the diagram correspond to positive (inductive) and negative
(capacitive) reactive components of the impedance, respectively.
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Example: Reflection coefficients in the Smith chart
If the measured quantity is a complex reflection coefficient
Γ
(e.g. S
11
, S
22
), then the unit Smith chart
can be used to read the normalized impedance of the DUT. The coordinates in the normalized
impedance plane and in the reflection coefficient plane are related as follows (see also: definition of
matched-circuit (converted) impedances):
Z / Z
0
= (1 +
Γ
) / (1 –
Γ
)
From this equation it is easy to relate the real and imaginary components of the complex resistance to
the real and imaginary parts of
Γ
[
]
,
)
Im(
)
Re(
1
)
Im(
)
Re(
1
/ )
Re(
2
2
2
2
0
Γ
+
Γ
−
Γ
Γ −
−
=
=
Z Z
R
[
]
,
)
Im(
)
Re(
1
)
Im(
2
/ )
Im(
2
2
0
Γ
+
Γ
−
Γ
⋅
=
=
Z Z
X
in order to deduce the following properties of the graphical representation in a Smith chart:
•
Real reflection coefficients are mapped to real impedances (resistances).
•
The center of the
Γ
plane (
Γ
= 0) is mapped to the reference impedance Z
0
, whereas the circle
with |
Γ
| = 1 is mapped to the imaginary axis of the Z plane.
•
The circles for the points of equal resistance are centered on the real axis and intersect at Z =
infinity. The arcs for the points of equal reactance also belong to circles intersecting at Z = infinity
(open circuit point (1,0)), centered on a straight vertical line.
Circles of equal
resistance
Arcs of equal
reactance
Open-circuited
load (Z = infinity)
Short-circuited
load (Z = 0)
Matching
impedance (Z = Z
0
)
Examples for special points in the Smith chart:
•
The magnitude of the reflection coefficient of an open circuit (Z = infinity, I = 0) is one, its phase
is zero.
•
The magnitude of the reflection coefficient of a short circuit (Z = 0, U = 0) is one, its phase is –
180
0
.
Inverted Smith Chart
The inverted Smith chart is a circular diagram that maps the complex reflection coefficients S
ii
to
normalized admittance values. In contrast to the polar diagram, the scaling of the diagram is not linear.
The grid lines correspond to points of constant conductance and susceptance.
•
Points with the same conductance are located on circles.
•
Points with the same susceptance produce arcs.
The following example shows an inverted Smith chart with a marker used to display the stimulus value,
the complex admittance Y = G + j B and the equivalent inductance L (see marker format description in
the help system).
Documents you may be interested
Documents you may be interested
