Opens a submenu to view the measurement results as a function of time. The time domain transformation requires option ZVAB-K2, Time Domain.
Time domain transformation
The network analyzer measures and displays complex S-parameters and other quantities as a function of the frequency. The measurement results can be filtered and mathematically transformed in order to obtain the time domain representation, which often gives a clearer insight into the characteristics of the DUT.
Time domain transforms can be calculated in band pass or low pass mode. For the latter the analyzer offers the impulse and step response as two alternative transformation types. A wide selection of windows can be used to optimize the time domain response and suppress sidelobes due to the finite sweep range. Moreover, it is possible to eliminate unwanted responses by means of a time gate and transform the gated result back into the frequency domain.
For a detailed discussion of the time domain transformation including many examples refer to the application note 1EZ44_OE which is posted on the R&S internet.
Frequency Domain and Time Domain select frequency domain or time domain representation of the active trace.
Time Domain Stimulus Axis opens a submenu to define the stimulus axis range for the time domain representation.
Define Transform... opens a dialog to define the transformation type and the frequency domain window used to optimize the time domain response.
Time Gate switches the time gate defined with Define Time Gate... on or off.
Define Time Gate... opens a dialog to select the time gate and define its parameters.
Selects the frequency domain representation for the active trace. The softkey is enabled if option ZVAB-K2, Time Domain, is available, and if a linear frequency sweep (Channel – Sweep – Sweep Type – Lin. Frequency) is active.
In frequency domain representation the diagram shows the measured trace as a function of the stimulus frequency applied to the DUT. The trace corresponds to the results obtained during the frequency sweep, however, the effect of a time gate is taken into account as long as the Time Gate function is active. The x-axis corresponds to the sweep range (stimulus range) selected via Channel – Stimulus.
Gated and ungated state of the frequency domain representation
The trace in the frequency domain depends on the state of the Time Gate:
If the gate is disabled, the frequency domain (FD) trace corresponds to the sweep results prior to the transformation.
If the gate is enabled, the frequency domain trace shown is calculated from the time domain (TD) trace which is gated and transformed back into the frequency domain.
The analyzer uses fixed No Profiling (Rectangle) window settings to transform the measured trace into time domain. The TD trace is gated using the selected time gate. The gated trace is transformed back into frequency domain using a No Profiling (Rectangle) window.
The shape, width and position of the time gate affect the gated frequency domain trace. The window type selection in the Define Transform dialog is ignored. The selected window is used again when the TD trace is displayed (Time Domain: On).
The rectangular No Profiling (Rectangle) windows minimize numerical inaccuracies near the boundaries of the measured frequency span. In the limit where the effect of the time gate vanishes (e.g. a gate of type Notch and a very small width), the time gated trace is equal to the original measured trace.
In time domain representation, you can use the Time Gate settings in order to eliminate unwanted responses in your signal. After switching back to the frequency domain, you will receive the frequency response of your DUT without the contribution of the unwanted responses.
Setting up a time domain measurement
Using a time gate
Remote control:
CALCulate<Chn>:TRANsform:TIME:STATe OFF
Selects the time domain representation for the active diagram area. The softkey is enabled if option ZVAB-K2, Time Domain, is available, and if a linear frequency sweep (Channel – Sweep – Sweep Type – Lin. Frequency) is active. The analyzer automatically quits time domain representation as soon as a different sweep type is selected.
In time domain representation the diagram shows the measurement results as a function of time. The results are obtained by transforming the measured frequency sweep data into the time domain using an appropriate mathematical transformation type and frequency window (Define Transform...). The sweep range and the output power for the active channel is still displayed below the diagram; the displayed time interval is shown in a second line:
Trace settings in time domain representation
While the time domain representation is active the trace settings behave as follows:
The settings in the Time Domain Stimulus Axis submenu configure the time axis.
All Trace Formats including the circular diagrams are available.
Limit lines can be defined like the limit lines for time sweeps.
The bandfilter search functions are available for the transformed trace.
If marker coupling is active, then the markers in the time domain and in the frequency domain are coupled with each other.
The analyzer places no restriction on the measured quantities to be transformed into the time domain. Impedances and admittances are first converted back into the equivalent S-parameter, transformed, and restored after the transformation.
Properties of the Chirp z-transformation
The Chirp z-transformation that the analyzer uses to compute the time domain response is an extension of the (inverse) Fast Fourier Transform (FFT). Compared to the FFT, the number of sweep points is arbitrary (not necessarily an integer power of 2), but the computation time is increased by approx. a factor of 2. This increased computation time is usually negligible compared to the sweep times of the analyzer.
The following properties of the Chirp z-transformation are relevant for the analyzer settings:
The frequency points must be equidistant.
The time domain response is repeated after a time interval which is equal to Δt = 1/Δf, where Δf is the spacing between two consecutive sweep points in the frequency domain. For a sweep span of 4 GHz and 201 equidistant sweep points, Δf = 4 GHz/200 = 2 * 107 Hz, so that Δt = 50 ns. Δt is termed measurement range (in time domain) or unambiguous range.
Additional constraints apply if the selected Chirp z-transformation is a lowpass transformation.
CALCulate<Chn>:TRANsform:TIME:STATe ON
Opens a submenu to define the stimulus axis range for time domain representation.
Start Time Domain is the lowest displayed time and corresponds to the left edge of the Cartesian diagram.
Stop Time Domain is the highest displayed time and corresponds to the right edge of the Cartesian diagram.
Center Time Domain corresponds to the center of the Cartesian diagram, i.e. (Start + Stop)/2.
Span Time Domain corresponds to the diagram width, i.e. (Stop – Start).
Time and Distance switch over between the x-axis scaling in time units or distance units.
Mechanical Length opens the dialog which defines port-specific offset parameters (mechanical length, velocity factor, loss); see Mechanical Length. The velocity factor affects the relationship between distance and time units; see background information below.
Use the paste marker list for convenient entry of Start and Stop values.
Distance units for transmission and reflection parameters
The interpretation of time and distance depends on the measurement type. For reflection measurements, the time axis represents the propagation time of a signal from the source to the DUT and back. For transmission measurement, it represents the propagation time from the source through the device to the receiver. The Distance calculation is consistent with this interpretation:
For reflection measurements (S-parameters Sii or ratios with equal port indices) the distance between the source and the DUT is half the propagation time multiplied by the velocity of light in the vacuum times the velocity factor of the receiving port defined in the Channel – Offset menu (Distance = 1/2 * Time * c0 * Velocity Factor). The factor 1/2 accounts for the return trip from the DUT to the receiver.
For transmission measurements, the distance is calculated as the propagation time times the velocity of light in the vacuum times the velocity factor of the receiving port defined in the Channel – Offset menu (Distance = Time * c0 * Velocity Factor).
Due to the properties of the Chirp z-transformation the trace is periodic in time and repeats after an unambiguous range of Δt = 1/Δf, where Δf is the spacing between two consecutive frequency points. To extend the unambiguous range, either reduce the sweep span (Channel – Stimulus) or increase the number of sweep points.
CALCulate<Chn>:TRANsform:TIME:STARt CALCulate<Chn>:TRANsform:TIME:STOP CALCulate<Chn>:TRANsform:TIME:CENTer CALCulate<Chn>:TRANsform:TIME:SPAN CALCulate<Chn>:TRANsform:TIME:XAXis TIME | DISTance
The Define Transform dialog selects the transformation type and the frequency domain window which is applied to the trace in order to optimize its time domain response.
The radio buttons in the Type panel select a band pass or low pass transform. To calculate a low pass transform the sweep points must be on a harmonic grid (otherwise the analyzer will only be able to calculate an approximate result and generate a warning). Low Pass Settings... opens a dialog to establish or change a harmonic grid (not available for memory traces).
The Impulse Response panel shows the impulse response of a constant trace over a finite sweep range (i.e. a rectangular function) that was filtered in the frequency domain using different windows. The selected window is applied to the active trace. The analyzer always uses a No Profiling (Rectangle) window to calculate the time-gated frequency domain trace, see background information in section Frequency Domain.
If an Arbitrary Sidelobes (Dolph-Chebychev) window is selected, the Arbitrary Sidelobe Level (sidelobe suppression) can be set below the Impulse Response diagrams. The entered value is the ratio of the power of the central lobe to the power of the first side lobe in dB.
The Resolution Enhancement Factor broadens the frequency range that the analyzer considers for the time domain transform by a linear factor. A factor of 1 means that the original sweep range and the measured sweep points are used; no additional assumptions are made. With higher resolution enhancement factors, the measurement data is extrapolated using a linear prediction method. As a result, the resolution in time domain can be improved. The ideal resolution enhancement factor depends on the properties of the DUT. In distance to fault measurements on cables, factors between 3 and 5 turned out to be a good choice.
For a comparison of the different transformation types and windows and for application examples please also refer to the application note 1EZ44_OE which is posted on the R&S internet.
The frequency domain window is used to filter the trace prior to the time domain transformation. An independent Time Gate can be used after the transformation in order to eliminate unwanted responses.
CALCulate<Chn>:TRANsform:TIME[:TYPE] CALCulate<Chn>:TRANsform:TIME:STIMulus CALCulate<Chn>:TRANsform:TIME:WINDow CALCulate<Chn>:TRANsform:TIME:DCHebyshev CALCulate<Chn>:TRANsform:TIME:RESolution:EFACtor
The analyzer provides two essentially different types of time domain transforms:
Band pass mode : The time domain transform is based on the measurement results obtained in the sweep range between any set of positive start and stop values. The sweep points must be equidistant. No assumption is made about the measurement point at zero frequency (DC value). The time domain result is complex with a generally undetermined phase depending on the delay of the signal.
Low pass mode : The measurement results are continued towards f = 0 (DC value) and mirrored at the frequency origin so that the effective sweep range (and thus the response resolution) is more than doubled. Together with the DC value, the condition of equidistant sweep points implies that the frequency grid must be harmonic. Due to the symmetry of the trace in the frequency domain, the time domain result is harmonic.
The band pass and low pass modes are compared below.
Transform type
Band pass
Low pass
Advantages
Easiest to use: works with any set of equidistant sweep points
Higher response resolution (doubled)
Includes information about DC value
Real result
Impulse and step response
Restrictions
No step response
Undetermined phase
Needs harmonic grid
Use for...
Scalar measurements where the phase is not needed
DUTs that don't operate down to f = 0 (e.g. pass band or high pass filters)
Scalar measurements where the sign is of interest
DUT's with known DC value
CALCulate<Chn>:TRANsform:TIME[:TYPE]
In low pass mode, the analyzer can calculate two different types of responses:
The impulse response corresponds to the response of a DUT that is stimulated with a short pulse.
The step response corresponds to the response of a DUT that is stimulated with a voltage waveform that transitions from zero to unity.
The two alternative responses are mathematically equivalent; the step response can be obtained by integrating the impulse response:
Integrate impulse response
Obtain step response
The step response is recommended for impedance measurements and for the analysis of discontinuities (especially inductive and capacitive discontinuities). The impulse response has an unambiguous magnitude and is therefore recommended for most other applications.
CALCulate<Chn>:TRANsform:TIME:STIMulus
The finite sweep range in a frequency domain measurement with the discontinuous transitions at the start and stop frequency broadens the impulses and causes sidelobes (ringing) in the time domain response. The windows offered in the Define Transform dialog can reduce this effect and optimize the time domain response. The windows have the following characteristics:
Window
Sidelobe suppression
Relative impulse width
Best for...
No Profiling (Rectangle)
13 dB
1
–
Low First Sidelobe (Hamming)
43 dB
1.4
Response resolution: separation of closely spaced responses with comparable amplitude
Normal Profile (Hann)
32 dB
1.6
Good compromise between pulse width and sidelobe suppression
Steep Falloff (Bohman)
46 dB
1.9
Dynamic range: separation of distant responses with different amplitude
Arbitrary Sidelobes (Dolph-Chebychev)
User defined between 10 dB and 120 dB
1.2 (at 32 dB sidelobe suppression)
Adjustment to individual needs; tradeoff between sidelobe suppression and impulse width
CALCulate<Chn>:TRANsform:TIME:WINDow CALCulate<Chn>:TRANsform:TIME:DCHebyshev
The Low Pass Settings dialog defines the harmonic grid for low pass time domain transforms.
Harmonic grid
A harmonic grid is formed by a set of equidistant frequency points fi (i = 1...n) with spacing Δf and the additional condition that f1 = Δf. In other words, all frequencies fi are set to harmonics of the start frequency f1.
If a harmonic grid, including the DC value (f = 0) is mirrored to the negative frequency range, the result is again an equidistant grid.
The point symmetry with respect to the DC value makes harmonic grids suitable for lowpass time domain transformations.
The dialog can be used to change the current grid of sweep points, which may or may not be harmonic.
The three buttons in the Set Harmonic Grid... panel provide alternative algorithms for calculation of a harmonic grid, based on the current sweep points.
The control elements in the DC Value panel define the measurement result at zero frequency and in the interpolation/extrapolation range between f = 0 and f = fmin. They are enabled after a harmonic grid has been established.
Defining the low frequency sweep points
After calculating a harmonic grid, the analyzer must determine the value of the measured quantity at zero frequency and possibly at additional points in the range between f = 0 and f = fmin.
The following figure shows a scenario where the harmonic grid was calculated with fixed Stop Frequency and Number of Points. The DC value and the values at the two additional red points must be extrapolated or interpolated according to the measured sweep points (blue dots) and the properties of the DUT.
If the properties of the DUT at f = 0 are sufficiently well known, then it is recommendable to enter the DC value manually (Manual Entry) and let the analyzer calculate the remaining values (red dots) by linear interpolation of the magnitude and phase(Examples: At f = 0 the reflection factor of an open-ended cable is 1. It is –1 for a short-circuited cable and 0 for a cable with matched termination. If a cable with known termination is measured, then these real numbers should be entered as DC values.).Clicking the Extrapolate button will initiate an extrapolation of the measured trace towards f = 0 and overwrite the current DC value. This can be used for a consistency check.
Continuous Extrapolation initiates an extrapolation of the measured trace towards lower frequencies, so that the missing values (green and red dots) are obtained without any additional input. The extrapolation is repeated after each sweep.
CALCulate<Chn>:TRANsform:TIME:LPASs KFSTop | KDFRequency | KSDFrequency CALCulate<Chn>:TRANsform:TIME:LPASs:DCSParam CALCulate<Chn>:TRANsform:TIME:LPASs:DCSParam:CONTinuous CALCulate<Chn>:TRANsform:TIME:LPASs:DCSParam:EXTRapolate CALCulate<Chn>:TRANsform:TIME:LPFRequency
In the Set Harmonic Grid... panel of the Low Pass Settings dialog, a harmonic grid can be calculated in three alternative ways:
Keep Stop Frequency and Number of Points calculates a harmonic grid based on the current stop frequency (Channel – Stimulus – Stop) and the current number of sweep points (Channel – Sweep – Number of Points). This may increase the frequency gap (the spacing between the equidistant sweep points, i.e. the sweep Span divided by the Number of Points minus one).
Keep Frequency Gap and Number of Points calculates a harmonic grid based on the current stop frequency (Channel – Stimulus – Stop) and the current frequency gap.
Keep Stop Frequency and Approximate Frequency Gap calculates a harmonic grid based on the current stop frequency (Channel – Stimulus – Stop), increasing the number of points (Channel – Sweep – Number of Points) in such a way that the frequency gap remains approximately the same. This may increase the sweep time, due to the additional sweep points introduced.
The three grids can be calculated repeatedly in any order; the analyzer always starts from the original set of sweep points.
Visualization of the harmonic grid algorithms
The three types of harmonic grids have the following characteristics:
Keep Stop Frequency and Number of Points means that the stop frequency and the number of sweep points is maintained. The sweep points are re-distributed across the range between the minimum frequency of the analyzer and the stop frequency; the step width may be increased.
Keep Frequency Gap and Number of Points means that the number of sweep points and their relative spacing is maintained. If the start frequency of the sweep is sufficiently above the fmin, the entire set of sweep points is shifted towards lower frequencies so that the stop frequency is decreased.
If the start frequency of the sweep is close to fmin, then the sweep points may have to be shifted towards higher frequencies. If the last sweep point of the calculated harmonic grid exceeds the maximum frequency of the analyzer, then an error message is displayed, and another harmonic grid algorithm must be used.
Keep Stop Frequency and Approximate Frequency Gap means that the stop frequency is maintained and the number of sweep points is increased until the range between fmin and the stop frequency is filled. The frequency gap is approximately maintained.
The figures above are schematic and do not comply with the conditions placed on the number of sweep points and interpolated/extrapolated values.
The harmonic grids can not be calculated for any set of sweep points. If the minimum number of sweep points is smaller than 5, then the interpolation/extrapolation algorithm for additional sweep points will not work. The same is true if the number of sweep points or stop frequency exceeds the upper limit. Besides, the ratio between the sweep range and the interpolation range between f = 0 and f = fmin must be large enough to ensure accurate results. If the sweep range for the harmonic grid exceeds the frequency range of the current system error correction, a warning is displayed.
Finding the appropriate algorithm
The three types of harmonic grids have different advantages and drawbacks. Note that for a bandpass transformation the grid parameters have the following effect:
A wider sweep range (i.e. a larger bandwidth) increases the time domain resolution.
A smaller frequency gap extends the unambiguous range.
A larger number of points increases the sweep time.
With default analyzer settings, the difference between the grid types are small. The following table helps you find the appropriate grid.
Grid type: Keep
Sweep time
Time domain resolution
Unambiguous range
Algorithm fails if...
Stop freq. and no. of points
Freq. gap and no. of points
Stop frequency beyond upper frequency limit
Stop freq. and approx. freq. gap
Number of sweep points beyond limit
CALCulate<Chn>:TRANsform:TIME:LPASs KFSTop | KDFRequency | KSDFrequency
Switches the time gate defined via Define Time Gate on or off. An active time gate acts on the trace in time domain as well as in frequency domain representation. Gat is displayed in the trace list while the time gate is active.
The time gate is independent of the frequency window used to filter the trace prior to the time domain transformation.
In time domain representation, you can use the time gate settings in order to eliminate unwanted responses in your signal. After switching back to the frequency domain, you will receive the frequency response of your DUT without the contribution of the unwanted responses.
CALCulate<Chn>:FILTer[:GATE]:TIME:STATe <Boolean>
The Define Time Gate defines the properties of the time gate used to eliminate unwanted responses that appear on the time domain transform.
Start and Stop or Center and Span define the size of the time gate. The analyzer generates a warning if the selected time span exceeds the unambiguous range which is given by Δt = 1/Df, where Δf is the spacing between two consecutive frequency points. Simply reduce the time span until the warning disappears.
The filter Type defines what happens to the data in the specific time region. A Band Pass filter passes all information in the specified time region and rejects everything else. A Notch filter rejects all information in the specified time region and passes everything else.
If the Show Gate Limits after Closing this Dialog check box is selected two red lines indicating the start and stop of the time gate are permanently displayed in the diagram area.
The Gate Shape panel visualizes how the time gate will affect a constant function after transformation back into the frequency domain. The selected window is applied to the active trace. The two red vertical lines represent the Start and Stop values defining the size of the time gate. The analyzer always uses a Steepest Edges (Rectangle) window to calculate the time-gated frequency domain trace, see background information is section Frequency Domain.
If an Arbitrary Gate Shape (Dolph-Chebychev) window is selected, the Arbitrary Sidelobe Level can be set below the Gate Shape diagrams.
Comparison of time gates
The properties of the time gates are analogous to the properties of the frequency domain windows. The following table gives an overview:
Passband ripple
Steepest Edges (Rectangle)
0.547 dB
Eliminate small distortions in the vicinity of the useful signal, if demands on amplitude accuracy are low
Steep Edges (Hamming)
0.019 dB
Good compromise between edge steepness and sidelobe suppression
Normal Gate (Hann)
0.032 dB
Maximum Flatness (Bohman)
0 dB
Maximum attenuation of responses outside the gate span
Arbitrary Gate Shape (Dolph-Chebychev)
0.071 dB
Adjustment to individual needs; tradeoff between sidelobe suppression and edge steepness
CALCulate<Chn>:FILTer[:GATE]:TIME:STARt CALCulate<Chn>:FILTer[:GATE]:TIME:STOP CALCulate<Chn>:FILTer[:GATE]:TIME:CENTer CALCulate<Chn>:FILTer[:GATE]:TIME:SPAN CALCulate<Chn>:FILTer[:GATE]:TIME[:TYPE] BPASs | NOTCh CALCulate<Chn>:FILTer[:GATE]:TIME:SHOW CALCulate<Chn>:FILTer[:GATE]:TIME:WINDow RECT | HAMMing | HANN | BOHMan | DCHebyshev CALCulate<Chn>:FILTer[:GATE]:TIME:DCHebyshev