DE102013213296A1 - Method and measuring device for characterizing an emitting test object - Google Patents

Abstract

The measuring device (20) is used to characterize a measurement object (4) which sends out an emission signal on at least one emission frequency (ωDUT). The measuring device (20) comprises a signal generator (22) which injects an injection signal at an injection frequency (ωDUT + Δω) adjacent to the emission frequency (ωDUT) of the device under test (4) into the device under test (4) so that the emission signal and the injection signal are brought to superposition. The measuring device (20) also has an evaluation unit (50) which evaluates the resulting superimposed signal with regard to all frequency components, both with regard to amplitude and with regard to phase.

Description

The invention relates to a method and a measuring device for characterizing a measurement object which itself emits a signal and therefore can only be measured with difficulty. The method is used in particular for determining the reflection coefficient of the measurement object, in particular at or in the vicinity of the frequency of its emission signal.

The reflection behavior of high-frequency and microwave circuits is described by their reflection coefficient. The reflection coefficient is the ratio of reflected to incident wave and can be expressed in scalar notation, i. H. represented as a ratio of the amplitudes, as well as complex involving the phase rotation. Reflection coefficients are usually frequency-dependent, this applies in particular to their phase angle. For this reason, measured values must be supplemented by the measuring frequency or, within the scope of specifications, reference must be made to the associated frequency range. Reflection measurements today are predominantly performed with vectorial network analyzers (VNA), which both provide the stimulus signal and measure the complex wave ratio.

Reflection coefficients are defined for inputs and outputs, but the metrological detection at outputs can cause considerable difficulties. This is especially the case when the normal, d. H. Even without stimulus existing output signal can not be switched off or deliberately remain switched on, z. B. to measure the reflection behavior under operating conditions.

For these cases there are two basic procedures, whereby the measurement always takes place only at or in the immediate vicinity of the frequency of the output signal:
One possibility is to load the output of the source with different impedances, and measure the changing output power. Depending on how the load change is made and how the power measurement is made, the reflection coefficient of the source can be determined either scalar or vectorially. After this fundamental principle z. B. in the US 7,868,624 B2 described vectorial method.

Another possibility is the injection of a stimulus signal with a low frequency offset to the output frequency in the output of the signal source and the evaluation of the envelope of the resulting emergent wave in the time domain. According to this principle works in Förster, H.-J .: "Measurement of source match for broadband synthesizers and amps", Microwave Eningering Europe, December / January 1993, pages 41-46 , described scalar beat method, which belongs to the frequency offset method.

Other frequency offset methods which evaluate the output of the signal source in the frequency domain, be it scalar with a spectrum analyzer or vectorially with a network analyzer (conventional hot S-parameter measurement), fail to measure at level controlled sources. Namely, level-controlled sources respond to the injection of a stimulus signal not only with a reflected signal at that frequency but also with a mirror signal at ω _DUT -Δω (ω _DUT : frequency of the normal output signal; Δω: frequency offset of the stimulus signal). As will be shown later, all three frequency components of the output signal must be considered in-phase, if the reflection coefficient of a level-controlled source in the frequency domain is to be determined. Because of the lack of ability to measure phase angles, spectrum analyzers are basically ruled out. For network analyzers this possibility has not been used, probably because of ignorance of the other sideband.

The object of the invention is to provide a method and a measuring device for characterizing a test object which itself emits an emission signal, in particular for determining the reflection coefficient of the test object at or in the vicinity of its emission frequency.

The object is achieved with respect to the method by the features of claim 1 and with respect to the measuring device by the features of claim 11. The dependent claims contain advantageous developments of the invention.

The invention is based on the finding that an accurate characterization of the measurement object in the vicinity of its emission frequency, in particular an accurate determination of the reflection coefficient in the vicinity of the emission frequency, is only possible if an evaluation of all relevant frequency components takes place according to amount and phase when using the frequency offset method , The purely scalar evaluation of the beat signal known from the prior art, d. H. the sole measurement of the amplitude maxima and minima is too inaccurate.

The evaluation of the reflection coefficient is preferably carried out by measuring the ratio of the waves emitted by the measurement object and the waves injected into the measurement object both at the injection frequency and at an image frequency which mirrors the injection frequency at the emission frequency. The evaluation formula then also contains an initially indeterminate transformation factor, which can be determined if, in addition, the wave received at the emission frequency of the measurement object is evaluated.

Higher accuracy can be achieved by taking into account the fact that parts of the waves emitted by the test object are reflected in the measuring instrument and additionally injected into the test object. There, a further reflection and thus a change in the originally emitted by the measurement object waves. So if you measure the total injected waves, d. H. In particular, with additional consideration of the portions injected at the image frequency, the accuracy is further increased in a preferred embodiment.

The evaluation is preferably carried out in the baseband. It will be shown later that the evaluation in the baseband is equivalent to a high-frequency evaluation.

By varying the distance of the injection frequency at which the measuring device injects its signal into the measurement object from the emission frequency at which the measurement object emits, both the control bandwidth of a controller present in the measurement object and its temporal transient response can be determined.

Separate filters and detectors are preferably provided for the individual measuring frequencies, and a frequency offset takes place via corresponding mixers, so that in each case only the respective wave is evaluated at the corresponding detector. After the evaluation preferably takes place in the baseband, it is preferably carried out after the analog / digital conversion. The corresponding oscillators, mixers, filters and detectors may therefore be digitally designed, i. H. the oscillators are numerical oscillators and the mixers are preferably corresponding multipliers, while the filters are preferably respective digital FIR filters or IIR filters.

The advantage of the method according to the invention is that vectorial adaptation measurements on level-controlled sources are now possible with a standard measuring device, the vectorial network analyzer. All other methods have the disadvantage that special equipment and above all appropriate know-how is required to successfully perform this measuring task.

Preferred embodiments of the invention will be described below by way of example and with reference to the drawings. In the drawing show:

1 a block diagram of an example of an emissive measuring object to be measured, which has a level control;

2a a diagram for explaining the components which determine the reflection coefficient of the measuring object and the measuring device;

2 B a diagram for explaining the components which determine the reflection coefficient of the measurement object and the measuring device of the measurement object.

3 a diagram for explaining the frequency position of the individual signal components;

4 a diagram for explaining the phase position of individual signal components at steady level controller of the measurement object;

5 a diagram for explaining the phase position of individual signal components after the start of the control process of the level controller of the measuring object;

6 a diagram for explaining the frequency position of individual signal components;

7 a diagram for explaining the correction of the wave sizes;

8th a block diagram of a preferred embodiment of the measuring device in the form of a vector network analyzer and

9 a diagram for explaining the procedure in the evaluation of the control bandwidth of the present in the measurement object level controller.

In 1 is a simplified block diagram of a typical DUT to be measured 4 shown. The DUT (device under test) called DUT has a signal generator 5 and an adjustable attenuator 6 or an adjustable amplifier. This is with the exit gate 7 via a level tap 8th connected. This may be, for example, a directional coupler. This one has the entrance gate 1 , the exit gate 2 and the level tap gate 3 , The at the level tap 8th tapped signal becomes a detector 9 supplied, which detects the level of the output signal. The detected signal becomes a control amplifier 10 supplied, which is designed in the embodiment as an I (integrating) controller. The control amplifier 10 includes in the embodiment a differential amplifier 11 , for example, an operational amplifier. The control signal is the inverting input of the differential amplifier 11 about the resistance 12 supplied during the non-inverting input, the reference variable, namely the desired value of the detector output voltage, in the form of a relative to the reference potential 13 connected voltage source U _is to _be supplied. Between the output of the differential amplifier 11 and its inverting input is a capacitor 14 that together with the resistance 12 Defines the time constant of the controller and thus the control bandwidth. The output signal becomes the control input 15 adjustable attenuator 6 fed. Overall, the measurement object has 11 thus via a control loop or control device 16 ,

The measuring task consists in particular of the complex reflection coefficient Γ _G at the gate 7 to investigate. In the case of passive measuring objects, this is the complex quotient of the due to reflection on the measuring object 4 emitted wave b _G to the in the test object 4 injected wave a _G In active DUTs, such as a level-regulated source, are the conditions more complex because the measurement object always emits a wave. That is through the 2a and 2 B described.

2a describes the relationships for the signal components of an active device under test at the emission frequency ω _DUT in the steady state, ie with active and closed-loop control in the case of a level-controlled source. The wave b _s is the wave emerging from the output of the object to be measured, Γ _T describes the reflection behavior of the load. As can be seen immediately, the ratio b _G / a _{G is} not an immediate measure of the reflection coefficient Γ _{G of} the signal source, because this ratio depends not only on the reflection coefficient Γ _{G of} the DUT, but above all on the reflection coefficient Γ _{T of} the load. Measuring method for Γ _G , which load the output of the measurement object with different reflection coefficients Γ _T for the measurement (for example, that in the patent US 7,868,624 B2 described method) take advantage of this fact.

To use with a stimulating meter, z. As a network analyzer to measure the reflection coefficient Γ _G , the stimulus frequency must deviate slightly from the emission frequency. This describes the 2 B for the signal components of an active, but not level-controlled measurement object in the immediate vicinity of the emission frequency ω _DUT , specifically at the frequency ω _DUT + Δω of the injection signal. Because of the small frequency separation from the emission frequency, it can be assumed that the reflection coefficient of the measurement object is identical to the reflection coefficient Γ _G at the emission frequency. As is readily apparent, the sought reflection coefficient Γ _G can be measured as a complex ratio b _G / a _G of reflected wave b _G to injected wave a _G (Hot S-parameter measurement).

On level controlled sources is 2 B not directly applicable, and although the complex quotient b _G / a _G measurable at the stimulus frequency ω _DUT + Δω may in some cases deviate considerably from the actual reflection coefficient Γ _G. This is because part of the expected reflection b _{G is} not at the stimulus frequency ω _DUT + Δω, but at the image frequency ω _DUT - Δω. So you also have to measure this signal component and add (after appropriate transformation) to the proportion of the stimulus frequency before the quotient b _G / a _G can be evaluated.

The mirror signal arises because one through the actuator 6 made modulation of the signal level leaves the signal phase unchanged, which in turn can only be represented by two symmetrical sidebands.

To distinguish from the reflection coefficient of the output gate 7 without control input, for example, at a frequency offset Δω far outside the control bandwidth, the reflection coefficient Γ _G measurable under the action of the level control is also referred to as the equivalent reflection coefficient.

According to the invention, to determine the impedance, the excitation signal (injection signal) with a frequency offset to the measurement object 4 given. The level detector 9 of the measurement object 4 now sees as input the superposition of the own generator signal and the excitation signal. The amplitude of this signal, a beat, is not constant, but changes periodically according to the frequency offset Δω. If the excitation signal is small in relation to the generator signal, the envelope of the beat has the same shape as an amplitude modulation, but in addition the phase is modulated.

Will now the scheme 16 is activated, the integrating controller attempts to make the output signal of the level detector as large as the reference variable U _soll , ie to compensate the level fluctuations. In this process, modulation of the generator signal occurs, namely amplitude modulation with two side lines, when the excitation signal is small compared to the generator signal. With a larger signal level, further side lines are created. This will be in 3 illustrated. 5 shows the beginning of the control process. The process is completed as soon as the two side lines have such an amplitude that a frequency-modulated oscillation having a time-independent amplitude is produced by the superposition with the excitation signal and the signal at the center frequency ω _DUT .

4 shows this situation with stabilized control as a vector diagram. If the level of the excitation signal is small compared to the generator signal, narrow band frequency modulation with only two sidelines results. With larger modulation, side lines are produced at integer multiples of the frequency offset Δω. Is in 3 shown on the example of the amplitude-modulated generator signal.

The resulting spectrum at the exit gate 7 is in 6 shown.

• – das amplitudenmodulierte Generatorsignal mit mindestens drei Frequenzkomponenten, und zwar bei der Mittenfrequenz ω_DUT und den Seitenbandfrequenzen ω_DUT – Δω und ω_DUT + Δω.
• – der vom Messobjekt reflektierte Anteil des Erregungs-Signals bei der Frequenz ω_DUT + Δω.

At the exit gate 7 of the DUT, the following signal components are emitted:

• - The amplitude-modulated generator signal having at least three frequency components, namely at the center frequency ω _DUT and the side band frequencies ω _DUT - Δω and ω _DUT + Δω.
• - The proportion of the excitation signal reflected by the measured object at the frequency ω _DUT + Δω.

Because the composition of the signal at the output port is typically different than at the level detector, it will have characteristics of amplitude and frequency modulation.

That on the exit gate 7 incident signal will primarily contain the excitation signal. The height of the other frequency components depends on how much the signals emitted by the measuring object are reflected back inside the measuring device (reflection coefficient Γ _T ).

To be able to measure the equivalent source reflection factor Γ _G , of course, the wave quantities must be detected simultaneously and system-corrected in the reference plane. A sequential measurement is not possible, as this leads to the loss of the phase relationship. The system error correction takes place in the usual way and is based on the known model of a vectorial network analyzer with a measuring port, which in 7 is illustrated. 7 shows how the sought wave sizes â and b ^ are linked to the measured raw wave quantities a and b.

8th shows the block diagram of a device according to the invention as a meter 20 trained vectorial network analyzer VNA. The measurement object 4 is with his exit goal 7 in the reference plane 21 connected. A signal generator 22 is via a directional coupler 23 with the measurement object 4 connected. A sample from the signal generator 22 generated signal is at the output 24 of the directional coupler 23 available and will have a mixer 25 mixed into baseband or in an intermediate frequency position and there via an analog / digital converter 26 digitized. That of the measurement object 4 received signal is at the output 27 of the directional coupler 23 available and will be over the mixer 28 mixed into baseband or in the intermediate frequency position and there via the analog / digital converter 29 digitized. To achieve the necessary phase coherence, both mixers 25 and 28 the first signal path 31 and the second signal path 30 preferably via a common local oscillator 32 provided.

A first example designed as a multiplier digital mixer 33 in the first signal path 31 is arranged, receives the output signal of the analog / digital converter 29 and the signal of a first digital oscillator 34 , which may be formed, for example, as a numerically controlled oscillator (NCO1). At its output is a first filter and detector block 35 , The frequency of the first oscillator 34 is set in such a way that the wave received at the injection frequency ω _DUT + Δω and transferred to the baseband (in 8th b ^ (f ₁ ), in the following mathematical consideration b ~ _{2_Δω} ) is detected.

A second preferably also as a multiplier trained digital mixer 36 in the first signal path 31 is arranged, also receives the output signal of the analog / digital converter 29 and the signal of a second digital oscillator 37 , which can also be designed as a numerically controlled oscillator (NCO3). At its exit is a second filter and detector block 38 , The frequency of the second oscillator 37 is set so that the wave received at the image frequency ω _DUT -Δω and transferred to the baseband (in 8th b ^ (f ₃ ), in the following mathematical consideration b ~ _{2_-Δω} ) is detected.

) detektiert wird.A third preferably likewise designed as a multiplier digital mixer 39 in the first signal path 31 is arranged, also receives the output signal of the analog / digital converter 39 and the signal of a third digital oscillator 40 , which can also be designed as a numerically controlled oscillator (NCO2). At its exit is a third filter and detector block 41 , The frequency of the third oscillator 40 is set so that the at the emission frequency ω _{DUT of} the measurement object 4 received and transferred to baseband wave (in 8th b ^ (f ₂ ), in the following mathematical consideration

) is detected.

In the second signal path 30 there is a fourth digital mixer 42 connected to the output of the analogue to digital converter 26 is connected and the signal of the fourth digital oscillator 43 (NCO1) receives. The output of the fourth mixer 42 is with the fourth filter and detector block 44 connected. The passband width of the fourth filter 44 is designed so that the associated detector 44 that from the signal generator 22 into the measurement object 4 injected signal at the frequency ω _DUT + Δω (in 8th a ^ (f ₁ ), in the following mathematical consideration a ~ _{2_Δω} ).

In the second signal path 30 there is also a fifth digital mixer 45 that also connected to the output of the analog to digital converter 26 is connected and the signal of the fifth digital oscillator 46 (NCO3) receives. The output of the fifth mixer 45 is with the fifth filter and detector block 47 connected. The passband width of the fifth filter 47 is designed so that the associated detector 47 that at the signal generator 22 reflected and returned to the measurement object 4 reinjected image frequency signal at the frequency ω _DUT - Δω (in 8th a ^ (f ₃ ), in the following mathematical consideration a ~ _{2_-Δω} ) detected.

The detected signal components b ^ (f ₁ ), b ^ (f ₂ ), b ^ (f ₃ ), a ^ (f ₁ ) and a ^ (f ₃ ) are in an evaluation unit 50 , For example, a CPU or an FPGA or an ASIC, evaluated, so that first a transformation factor γ ~ and finally the sought reflection coefficient is calculated. As shown in the mathematical analysis below.

9 illustrates the possibility by a different choice of the frequency spacing Δω of the emission frequency ω _{DUT of} the measurement object 4 the frequency response of the measured object 4 existing control device 16 to investigate. In each case, at the corresponding image frequency ω _DUT -Δω, the associated received wave quantity b 1 is measured. In 9 this is illustrated by four different frequency offsets. In practice, of course, is typically measured at significantly more measuring points. It determines the amplitude drop by a factor of 0.7, which corresponds to the usual definition of the bandwidth at 3 dB. By means of a corresponding Fourier transformation of the measured complex wave quantities b 1, it is also possible to draw conclusions about the time behavior of the control device 16 , ie on the transient response of the control device 16 , make.

aus Tor 2 des Pegelabgriffs 8 bei der Signalfrequenz ω_DUT austretende Welle

Komponente im Basisband

Komponente ohne Phasenterm e^j...
F(Δω) Übertragungsfunktion der Pegelregelschleife
γ Transformationsfaktor
γ ~ Komponente im Basisband
Γ_G äquivalenter Reflexionskoeffizient an Tor 2 des Pegelabgriffs 8
Γ ^_G Schätzwert für Γ_G
Γ_Q Reflexionskoeffizient der inneren Signalquelle (an Tor 1 des Pegelabgriffs 8 angeschlossen)
Γ_T Reflexionskoeffizient der Testquelle (an Tor 2 des Pegelabgriffs 8 angeschlossen)
S_xy S-Parameter des Dreitors (b_x/a_y)
s_c Seitenband des Quellensignals bei der Stimulusfrequenz
s_m Seitenband des Quellensignals bei der Spiegelfrequenz zum Stimulussignal
ω_g (Kreis-)Grenzfrequenz der Pegelregelschleife
x* zu x konjugiert komplexe ZahlIn the following, the evaluation formula for the measurement of the equivalent reflection coefficient Γ _{G is} derived and various simplifications are discussed. The following symbols are used in the following mathematical representation:
a _x on gate x ( 1 . 2 . 3 ) of the level tap 8th incident wave
a _{x_Q} component, which can be attributed to the source _signal b _Q
a ~ _{x_Q} component in baseband
a _{x_T} component, which can be attributed to the source _signal b _T
a ~ _{x_T} component in baseband
a _{2_ ± Δω} on goal 2 the level tap 8th at the frequency ω _TEST = ω _DUT ± Δω incident wave
a ~ _{2_ ± Δω} component in baseband
a ⁀ _{2_ ± Δω} component without phase term e ^{j ...}
b _Q from the at gate 1 the level tap 8th connected source when adapting outgoing wave (generator signal)
b _T out of the gate 2 the level tap 8th connected source when adapting outgoing wave (stimulus / test signal)
b _x from port x ( 1 . 2 . 3 ) of the level tap 8th emerging wave
b _{x_Q} component which can be attributed to the source _signal b _Q
b ~ _{x_Q} component in baseband
b _{x_T} component, which can be traced back to the source _signal b _T
b ~ _{x_T} component in baseband
b _{2_ ± Δω} out of gate 2 the level tap 8th at the frequency ω _DUT ± Δω emerging wave
b ~ _{2_ ± Δω} component in baseband
b ⁀ _{2_ ± Δω} component without phase term e ^{j ...}

out of gate 2 the level tap 8th at the signal frequency ω _DUT emerging wave

Component in the baseband

Component without phase term e ^{j ...}
F (Δω) transfer function of the level control loop
γ transformation factor
γ ~ component in baseband
Γ _G equivalent reflection coefficient at gate 2 the level tap 8th
Γ ^ _G estimate for Γ _G
Γ _Q Reflection coefficient of the internal signal source (at gate 1 the level tap 8th connected)
Γ _T Reflection coefficient of the test source (at Tor 2 the level tap 8th connected)
S _xy S parameters of the three-port (b _x / a _y )
s _c sideband of the source signal at the stimulus frequency
s _m sideband of the source signal at the image frequency to the stimulus signal
ω _g (circular) limit frequency of the level control loop
x * complex conjugate to x

The reflection coefficient of a level-controlled source according to 1 is exclusively a function of the S-parameters of the three-door ( 1 . 2 . 3 ) to the level tap: Γ _G = S ₂₂ - S ₃₂ S ₂₁ / S ₃₁ (1)

This applies to all controllers with integrating behavior, ie without a control remainder at the input of the level detector. To distinguish it from the reflection coefficient at the exit gate ( 2 ) without control input, the term "equivalent" reflection coefficient is often used.

To simplify the derivation, but without limiting the generality of the procedure, it is assumed that Tor 3 the level tap 8th may be completed without reflections, ie that it does not affect the rest of the circuit.

That in goal 1 injected generator _signal a _{1_Q} is at the gates 2 and 3 generate the following wave components: b _{2_Q} = S ₂₁ a _{1_Q} + S ₂₂ Γ _T b _{2_Q} (2) b _{3_Q} = S ₃₁ a _{1_Q} + S ₃₂ Γ _T b _{2_Q} (3)

By eliminating a _{1_Q} and inserting (1) one obtains after some transformations

That in goal 2 injected stimulus _signal a _{2_T} is at the gates 2 and 3 generate the following wave components: b _{2_T} = S ₂₁ a _{1_T} + S ₂₂ a _{2_T} (5) b _{3_T} = S ₃₁ a _{1_T} + S ₃₂ a _{2_T} (6)

und nach Eliminieren von a_{2_T}

With a _{1_T} = Γ _Q b _{1_T} (7) and b _{1_T} = S ₁₂ a _{2_T} + S ₁₁ Γ _Q b _{1_T} (8) obtained after eliminating a _{1_T} and b _{1_T}

and after eliminating a _{2_T}

The signal generator 5 At the level detector, let's take a sinusoidal RF signal with the amplitude 1 and the angular frequency ω _DUT generate, which is a test signal from the signal generator 22 with the amplitude k ∈ R (11) and the angular frequency ω _TEST = ω _DUT + Δω (12) superimposed:

The resulting beat signal will cause the control loop to amplitude modulate the signal source, which in turn reduces the amount of beat. The transient process comes to an end when the superimposition of the amplitude-modulated source signal and the test signal has become a purely phase-modulated oscillation, which a conventional level detector can not distinguish from a continuous, monofrequency signal. For the phase-modulated oscillation must apply:

After subtracting the test signal, which is still present, the source signal is again obtained, which has a pure amplitude modulation for m = k / 2, ie can actually be generated by the source:

Let k << 1 be assumed, so that no sidebands at multiples of the beat frequency Δω have to be taken into account.

As at the level detector, so also at the output gate ( 2 ) Signal components at all three frequencies, ie ω _DUT , ω _DUT - Δω and ω _DUT + Δω be present. These components are determined below:
The component at the frequency ω _DUT can be calculated from (13) and (4):

For the component at the image frequency of the test signal (ω _DUT - Δω), the following applies analogously:

berechnet aus (10) und (13), und dem Seitenband der Signalquelle bei ω_DUT + Δω, berechnet aus (4) und (13). In Summe erhält man

The component at the frequency of the test signal is composed of two parts: the reflection of the stimulus _signal a _{2_T} , ie

calculated from (10) and (13), and the sideband of the signal source at ω _DUT + Δω, calculated from (4) and (13). In total you get

The at Tor 2 incident wave of the test signal, which is needed as a reference for the reflection measurement, also consists of two components at the test frequency and a component at the image frequency together. For the stimulus signal at the test frequency, it follows from (9) and (18):

For this, the sideband of the source signal reflected at Γ _{T is} added at ω _DUT + Δω, which is calculated from equations (4) and (13) taking into account the reflection coefficient Γ _T :

After a few transformations you get

For the component at the image frequency of the test signal (ω _DUT - Δω), one obtains from (17):

In order to be able to process the sidebands b _{2_-Δω} and a _{2_-Δω} , these must be converted to the frequency ω _DUT + Δω. This is initially purely formal with the factor γ = e ^{j2 (Δωt + φ)} (24) happened:

An estimate for the sought reflection coefficient Γ _{G is} now defined as follows:

und für den Nenner

For the counter you get

and for the denominator

After a few transformations using equation (1), this yields Γ ^ _G = Γ _G , (30) ie the desired measurement result can be determined without error from the waves at the test port.

und wegen k ∊ RTo calculate the transformation term γ, the output signals to Tor 2 at the frequencies ω _DUT and ω _DUT - Δω needed. As you can easily understand, is true

and because of k ε R

As 8th 1, the signals at the three different frequencies are most easily obtained such that the digital values of the downsampled sum signals b ₂ and a ₂ (b and a in FIG 8th ) are converted into baseband with NCOs. They are represented there by complex number sequences z _i . If the LO frequencies of the NCOs were exactly equal to the actual frequencies, the baseband signals would be time independent. While this is true for the baseband component of ω _TEST , the stimulus frequency of the VNA, it is typically not for the baseband components of ω _DUT and ω _DUT - Δω. This may be because the difference frequency Δω to the signal source is either not known exactly or can not be set accurately enough. Nevertheless, a time-independent measurement result can be achieved, as shown below.

mit t' = t + Δt (34) The numerically controlled oscillators (NCOs) are designed to implement the input signals with the following functions, for the sake of simplicity, taking into account the first mixer stage and a temporal discretization of the signals:

With t '= t + Δt (34)

The time parameter .DELTA.t should represent the time offset between the system time t 'and the earlier introduced time t.

The term δω describes the estimation error for the LO frequency of this NCO.

It is essential for the function of the circuit according to the invention that the frequency offset between NCO3 and NCO1 be selected exactly twice as large as that between NCO2 and NCO1.

In the following, the signals mixed with the NCOs into the baseband are considered (for example, b ~ _{2_ + Δω corresponds to} the baseband _component of b _{2_ + Δω} ):

erhält man aus (39) und (41) sowie unter Verwendung von (31)

With the definition of the transformation factor γ ~

obtained from (39) and (41) and using (31)

So that applies

If the evaluation instruction (27) is transmitted to the signals of the baseband, the following exact evaluation formula for the reflection coefficient Γ _G results as expected:

zu gleichen Zeitpunkten aufgenommen und nur isotemporale Samples miteinander verrechnet werden.When there is a frequency error δω ≠ 0, the terms γ ~, b ~ _{2_-Δω} and a ~ _{2_-Δω become} time-dependent. Of course, this time dependence is no longer present in the final result, the reflection coefficient Γ _G. However, this assumes that the samples of the baseband signals b ~ _{2_-Δω} , a ~ _{2_-Δω} and

recorded at the same time points and only isotemporal samples are offset against each other.

The raw value of the reflection coefficient Γ _G determined with the calculation specifications (27) or (45) will deviate from the actual value Γ _G due to internal errors of the network analyzer. These errors cause the ratio of incident to outgoing wave is not determined exactly. However, the known correction methods, which are based on the three error terms directivity, source gate adaptation and reflection tracking, as well as the raw wave ratio, may also be used in the usual way. The final result leaves only very small residual errors on the part of the VNA.

The measurement can be simplified. In this case, a small measurement error occurs in connection with the adaptation of the VNA. The difference is that the wave a _{2_-Δω is} disregarded. Since the error is relatively small, but its elimination is associated with a fourth measurement channel, the lower accuracy is often accepted.

In evaluation equation (45) for the baseband signals and in the corresponding equation (27) for the high-frequency signals, the corresponding term is simply dropped. In the high-frequency level, then:

oder in guter Näherung

It follows

or in a good approximation

For many practical concerns, the absence of β plays no role. How to get along with | Γ _T | ≤ 0.25 for common network analyzers and | S ₃₂ S ₂₁ / S ₃₁ | ≤ 0.25 | Γ _Q S ₁₂ S ₂₁ | ≤ 0.06 for signal sources with a power splitter as the level tap a relative error β of less than 4%, which is quite sufficient for many applications.

The level control will normally cause any envelope modulation to disappear, ie the resulting sum signal pointer at the input of the level detector will move on a circular arc. In particular, when the factor k, which describes the ratio of the test / stimulus signal to the carrier signal at the input of the level detector, exceeds the value of about 0.1, this is only possible because side lines are also at ω _DUT ± nΔω (n ≥ 2) arise. For k = 1, for example, one would obtain the following relative (on the unmodulated carrier amplitude) related amplitudes of the side lines: n = 0 1 - k ^2/4 - 3 / 64k ⁴ = 0.70 n = 1 k / 2 = 0.50 n = 2 ^k2 / 8 + k ^4/32 = 0.16 n = 4 k ^4/64 = 0.016 stimulus k = 1.00

In the network analyzer measurement according to the method described, the higher side lines would not produce any measurement errors because the amplitude of the stimulus signal would continue to be in the ratio 2: 1 to the corresponding side line of the amplitude-modulated carrier oscillation (n = 0.50). The reduction of the carrier (to 70% of the initial value for k = 1) also did not matter, as well as the size k does not appear in the end result.

The scalar beat method would also work error free under the described conditions, but only as long as the sum signal at the level detector would be exclusively phase modulated. In practice, however, at least in the case of the scalar beat method, the rule would be that this condition is just not fulfilled: out of ignorance about the control bandwidth and out of ignorance about the factor k, which can only be determined by a spectral analysis of the amplitude ratio of Mirror sideband and carrier would be determined. Thus, if k were to be too small and significant side lines of higher order would have to arise, this could be prevented by a too small control bandwidth. Then the observable beat would be distorted, which in turn would cause the ratio of maxima to minima to be distorted. How big this error can be, can be easily estimated, if in the above example the amplitude ratio of the 2nd order sidelines to that 1st order forms: namely in the order of 30% to 40%.

The conditions in the method according to the invention are fundamentally different. Relative modulation and control bandwidth can both be easily determined via the proportionality factor k that arises anyway and its dependence on the frequency offset Δω and adjusted so that the control for the 1st order sidelines remains stable (always necessary) and the generation of higher order sidelines becomes reasonable Dimension remains limited, z. Furthermore, there would be no measurement error at all if the generation of higher-order side lines were omitted due to insufficient control bandwidth, precisely because the envelope, but only the first-order sidelines and the carrier for the phase information would be evaluated in γ ,

In conventional signal generators with integrated Stufenabschwächern the level control over the largest range of output power will be barely felt or not at all. Mathematically, the amplitude of the lateral line measurable at the image frequency is much smaller than that at the test frequency. This is the area where conventional network analyzers measure reasonably well. Network analyzers according to the invention also do this, but only with a large mirror line. In other words, the invention is suitable for all signal generators, whether the level control is strong, little or not noticeable in the reflection coefficient of the output.

The effect of insufficient control bandwidth will be discussed below.

The successful application of the method described requires that the sum signal at the level detector of the device under test (DUT) is exclusively phase-modulated and has no envelope modulation. For this condition to be fulfilled, the frequency offset Δω between the stimulus frequency and the signal frequency of the DUT must be significantly smaller than the bandwidth of the level control. Ideally, it would have to be made infinitesimally small, which would require accordingly narrowband sized low passes behind the NCOs. The resulting long settling times would not be acceptable. That's why you should preferably make the frequency offset so large that low passes with sufficiently high bandwidths can be used, which in turn then settle faster. The low-pass filters according to the NCOs are necessary so that the frequency components of the measurement signal which are not required in each case and which lie in the baseband at ± mΔω (m ∈ N) are sufficiently suppressed.

The described problem was already present in the scalar beat method, but the effects on the method according to the invention are much more serious. This is due to the fact that the control bandwidth is much more noticeable in the phase than in the amount of the measurement result. This will be explained in more detail below.

beschreiben, woraus für den Amplitudengang

und für den Phasengang

folgt. Für Δω = 0 gilt d|F(Δω)| / dΔω = 0 (49)

A level control can be considered simplified as a low-pass 1st order, a consequence of the integrating controlled system, which can actually always be assumed. The transfer function of the resulting 1st order low-pass lets through the equation

describe what the amplitude response is

and for the phase response

follows. For Δω = 0 applies d | F (Δω) | / dΔω = 0 (49)

This means that the phase error remains proportional to Δω even with small frequency offsets, while the amplitude error approaches the value zero much faster. An example should clarify that. A reflection coefficient of 0.3 is measured, and the required absolute error due to the bandwidth effect may not exceed 0.01 (3% in amplitude, 1.9 ° in phase). This is slightly more than the error contribution of modern VNAs after calibration with ordinary calibration kits. The control bandwidth, which is usually in the range of 1 kHz to 100 kHz, may be 10 kHz. It follows from the equations given that an amplitude error above the stated value only occurs at a frequency offset Δω / 2π of more than 2.6 kHz. In phase, this critical frequency is only 333 Hz, d. H. it is lower by a factor of ten. With an absolute error of 0.003 one would get 1.4 kHz or even only 100 Hz, d. H. the span would go further apart. The theoretically shortest possible measurement time (over exactly one period), the academic limit case so to speak, would amount to 700 μs for compliance with the error in the amplitude for the last-mentioned case, but 10 ms for compliance in phase. A sweep with 1000 measuring points would then run off in 0.7 s or 10 s. In fact, it should be a multiple of these values. The numbers speak for themselves, even considering that the control bandwidth can be less than 10 kHz.

The problem can only be solved by taking into account the frequency response of the phase detector in any way during the measurement, so that sufficiently large frequency offsets can be realized. Before the two possibilities according to the invention are discussed, the theoretical background will be briefly discussed.

The starting point are the equations (13) and (14). If the two sidebands of the source signal are referred to as s _c (equal to the test signal) or s _m (mirror signal), the following dependencies result from the incident wave of the test signal and the transfer function of the level control loop:

F (Δω) denotes the transfer function of the level control loop between the stimulus signal and the source's equal frequency sideband. If F (Δω) deviates from 1, then all those become Signal components at the VNA falsified, which originate from the two sidebands of the source signal. Phase and amplitude of the reflected test signal (via the parameter S ₂₂ ) are unaffected. This first means that the components b _{2_ + Δω} and a _{2_ + Δω} must be split at the frequency of the test signal before further processing. As can be easily understood, applies to the goal 2 emerging wave of the DUT reflected component of the test signal b _{2_T -b 2_ + Δω} γb _{2_-Δω} (53) b ~ _{2_T} = b ~ _{2_ + Δω} - γb _{2_-Δω} (54) and for the double bandwidth effect corrected sideline of the source signal at the test frequency

For the a waves you get: a _{2_T} - a _{2_ + Δω} - γa _{2_-Δω} (57) a ~ _{2_T} = a ~ _{2_ + Δω} - γ ~ a _{2_-Δω} (58)

bzw.

mit den Komponenten im Basisband.Thus, the calculation rule (27) goes over in

respectively.

with the components in baseband.

The definition or calculation rule for the transformation factor y (equations (32) and (42)) remains unchanged, but the resulting phase rotation is greater by + 2 · arg (F (Δω)) due to the bandwidth effect.

The equations (53) to (62) thus offer the possibility of compensating for the error caused by the bandwidth effect by taking into account the transfer function F (Δω) of the control loop. It is not necessary to know the entire function, but only the function value at the current frequency offset Δω.

The transfer function F (Δω) was implicitly defined by Equation (51) as the complex factor of 2 extended complex ratio of the sideline generated by the source at the test frequency to the equal frequency wave of the stimulus signal, both measured at the location of the level detector. Since the level detector for a measurement of F (Δω) is not accessible, the corresponding signals can only at the test port 2 be determined. Because of different transmission paths of both sizes, their ratio is at the test port 2 but unlike the level detector, so that a direct measurement of the absolute transfer function is not possible. Instead, this must be obtained via at least two ratio measurements:

The measurement of the ratio γ ~ b ~ _{2_-Δω} / a ~ _{2_T} at the operating frequency Δω is easily possible because all sizes are available. The real problem lies in the determination of the denominator term, because a setting Δω = 0 is not possible. For the magnitude of said ratio, the situation is relatively uncritical because the amplitude response remains at 1 for a long time (Equation 49), so accurate estimation for Δω = 0 is possible even at relatively high frequency offsets. In many cases, therefore, one could completely dispense with an amplitude correction and | F (Δω) | = 1.

In order to take account of the phase term arg (F (Δω)), however, one will usually be unable to avoid very precise measurements being made with large frequency offsets. Therefore, an accurate estimate of the phase angle is _required for the ratio γ ~ b ~ _{2_-Δω} / a ~ _{2_T} at Δω = 0. Either this measurement is actually performed for very small frequency offsets (takes a long time), or one makes the measurement at several higher frequencies and obtains an estimate for Δω = 0 by extrapolation. But the most elegant is a third way. As can be easily shown, applies F (-Δω) = F * (Δω), (64) ie arg [F (-Δω)] = -arg [F (Δω)]. (65)

This makes it possible to determine the phase angle at arbitrary, ie also very high frequency offsets Δω, simply by carrying out a second measurement in which the frequency offset of the stimulus signal changes sign. From the difference of the function values of γ ~ b ~ _{2_-Δω} / a ~ _{2_T} at + Δω and -Δω, the desired phase angle can be determined:

To avoid misunderstandings, it should be noted that b ~ _{2_-Δω} always means the component at the _{image frequency} to the stimulus signal, regardless of whether it occurs at + Δω or -Δω.

The invention is not limited to the illustrated embodiments. For example, it is not necessary to use the in 8th Although this is of course easier to implement, digital frequency mixer offsets and digital oscillators can be performed. The first oscillator 34 and the fourth oscillator 43 have the same frequency and can therefore be combined into a single oscillator. The same applies to the second oscillator 37 and the fifth oscillator 46 , Incidentally, all features of the invention described in the foregoing description and / or claimed in the following claims and / or illustrated in the drawings can be combined with each other as desired.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• US 7868624 B2 [0004, 0029]

Cited non-patent literature

• Förster, H.-J .: "Measurement of source match for broadband synthesizers and amps", Microwave Eningering Europe, December / January 1993, pages 41-46 [0005]

Claims (22)

Method for characterizing a test object ( 4 ), which emits an emission signal on at least one emission frequency (ω _DUT ), wherein by means of a measuring device ( 20 ) an injection signal at one of the emission frequency (ω _DUT ) of the measurement object ( 4 ) adjacent injection frequency (ω _DUT + Δω) in the measurement object ( 4 ) is injected so that the received signal and the injection signal are brought to overlap, and wherein both the amplitude and the phase of all frequency components of the beat signal are evaluated. A method according to claim 1, characterized in that in the evaluation of the reflection coefficient Γ _{G of} the measurement object ( 4 ) using the formula

is determined, where a ~ _{2_Δω} that of the measuring device ( 20 ) is at the injection frequency (ω _DUT + Δω) emitted wave, a ~ _{2_-Δω} on the measuring device ( 20 ) at an image frequency (ω _DUT - Δω), which is the injection frequency (ω _DUT + Δω) mirrored at the emission frequency (ω _DUT ), reflected and again into the measurement object ( 4 ) injected wave, b ~ _{2_Δω} that of the measuring device ( 20 ) at the injection frequency (ω _DUT + Δω), b ~ _{2_-Δω is} that received by the measuring device ( 20 ) at the image frequency (ω _DUT - Δω) is received, and γ ~ is a transformation factor. A method according to claim 1, characterized in that in the evaluation of the reflection coefficient Γ _{G of} the measurement object ( 4 ) using the formula

is determined in a simplified manner, where a ~ _{2_Δω} that of the measuring device ( 20 ) is at the injection frequency (ω _DUT + Δω) emitted wave, b ~ 2_Δω that of the measuring device ( 20 ) at the injection frequency (ω _DUT + Δω), b ~ _{2_-Δω is} that received by the measuring device ( 20 ) At the image frequency (ω _DUT - is a transformation factor Δω) that the (at the emission frequency ω _DUT) is mirrored injection frequency (ω + Δω _DUT), is received wave, and γ ~. A method according to claim 2 or 3, characterized in that in the evaluation of the transformation factor γ ~ using the formula

is determined, where

that of the meter ( 20 ) at the emission frequency (ω _DUT ) of the measurement object ( 4 ) received wave is and * stands for conjugate complex. Method according to one of claims 1 to 4, characterized in that the evaluation takes place after the of the measuring device ( 20 ) received waves by means of mixer ( 25 . 28 ) are shifted to baseband. Method according to one of claims 1 to 5, characterized in that the evaluation takes place after the by the measuring device ( 20 ) were corrected by means of correction matrices (G). Method according to one of Claims 1 to 5, characterized in that the correction by means of correction matrices (G) does not take place on the raw values of the received wave quantities but on the final result (Γ _G ) of the received waves. Method according to one of claims 1 to 7, characterized in that in the evaluation of the frequency response ( 60 ) one in the measurement object ( 4 ) existing control device ( 16 ) is determined by the distance (Δω) into the object to be measured ( 4 ) injected injection frequency (ω _DUT + Δω) of the emission frequency (ω _DUT ) of the measurement object ( 4 ) is varied. A method according to claim 8, characterized in that in the evaluation of the frequency response ( 60 ) in the object to be measured ( 4 ) existing control device ( 16 ) whose control bandwidth is determined by determining when the amplitude of the frequency response has dropped to a certain value, in particular has decreased by 3 dB. A method according to claim 8 or 9, characterized in that in the evaluation of the frequency response ( 60 ) in the object to be measured ( 4 ) existing control device ( 16 ) whose transient response is determined by performing a Fourier transform of the frequency response. Measuring device ( 20 ) for characterizing a measured object ( 4 ), which emits an emission signal on at least one emission frequency (ω _DUT ), wherein the measuring device ( 20 ) a signal generator ( 22 ) having an injection signal at one of the emission frequency (ω _DUT ) of the measurement object ( 4 ) adjacent injection frequency (ω _DUT + Δω) in the measurement object ( 4 ) are injected so that the emission signal and the injection signal are superimposed, and wherein the measuring device ( 20 ) an evaluation unit ( 50 ), which evaluates the pending overlay signal, and wherein the evaluation unit ( 50 ) evaluates both the amplitude and the phase of all frequency components of the beat signal. Measuring device according to claim 11, characterized in that the evaluation unit ( 50 ) the reflection coefficient Γ _{G of} the test object ( 4 ) using the formula

determined, where a ~ _{2_Δω} from the signal generator ( 22 ) at the injection frequency (ω _DUT + Δω), a ~ _{2_-Δω} is at the signal generator ( 22 ) at an image frequency (ω _DUT - Δω), which is the injection frequency (ω _DUT + Δω) mirrored at the emission frequency (ω _DUT ), reflected and again into the measurement object ( 4 ) injected wave, b ~ _{2_Δω} that of the measuring device ( 20 ) at the injection frequency (ω _DUT + Δω), b ~ _{2_-Δω is} that received by the measuring device ( 20 ) at the image frequency (ω _DUT - Δω) is received, and γ ~ is a transformation factor. Measuring device according to claim 11, characterized in that the evaluation unit ( 50 ) the reflection coefficient Γ _{G of} the test object ( 4 ) using the formula

simplified, where a ~ _{2_Δω} that from the signal generator ( 22 ) is at the injection frequency (ω _DUT + Δω) emitted wave, b ~ _{2_Δω} that of the measuring device ( 20 ) at the injection frequency (ω _DUT + Δω), b ~ _{2_-Δω is} that received by the measuring device ( 20 ) At an image frequency (ω _DUT - is a transformation factor Δω), which is the (at the emission frequency ω _DUT) mirrored injection frequency (ω + Δω _DUT), is received wave, and γ ~. Measuring device according to claim 12 or 13, characterized in that the evaluation unit ( 50 ) the transformation factor γ ~ using the formula

determined, where

the wave received by the meter at the emission frequency (ω _DUT ) of the _DUT is * complexed for conjugate. Measuring device according to one of claims 12 to 14, characterized in that between the signal generator ( 22 ) and a measuring gate ( 7 ), which with the measuring object ( 4 ), a directional coupler ( 23 ), one of the measuring object ( 4 ) incoming wave into a first signal path ( 31 ) and one of the signal generator ( 22 ) incoming wave into a second signal path ( 30 ) decoupled. Measuring device according to claim 15, characterized in that in the first signal path ( 31 ) a first mixer ( 33 ), a first oscillator ( 34 ), a first filter ( 35 ) and a first detector ( 35 ), wherein the frequency of the first oscillator ( 34 ) is set so that the of the measuring object ( 4 ) at the injection frequency (ω _DUT + Δω) received wave (b ~ _{2_Δω} ) by means of the first mixer ( 33 ) is offset in the frequency position so as to fit into the passband bandwidth of the first filter ( 35 ) and she is the first detector ( 35 ) detected. Measuring device according to claim 15 or 16, characterized in that in the first signal path ( 31 ) a second mixer ( 36 ), a second oscillator ( 37 ), a second filter ( 38 ) and a second detector ( 38 ), wherein the frequency of the second oscillator ( 37 ) is set so that the of the measuring object ( 4 ) at the image frequency (ω _DUT - Δω) received wave (b ~ _{2_-Δω} ) by means of the second mixer ( 36 ) is offset in the frequency position so as to fit into the passband width of the second filter ( 38 ) and they are the second detector ( 38 ) detected. Measuring device according to one of claims 15 to 17, characterized in that in the first signal path ( 31 ) a third mixer ( 39 ), a third oscillator ( 40 ), a third filter ( 41 ) and a third detector ( 41 ), wherein the frequency of the third oscillator ( 40 ) is set so that the of the measuring object ( 4 ) at the emission frequency (ω _DUT ) of the measurement object ( 4 ) received wave

by means of the third mixer ( 39 ) is offset in the frequency position so as to fit into the passband width of the third filter ( 41 ) and they are the third detector ( 41 ) detected. Measuring device according to one of claims 15 to 18, characterized in that in the second signal path ( 30 ) a fourth mixer ( 42 ), a fourth oscillator ( 43 ), a fourth filter ( 44 ) and a fourth detector ( 44 ), wherein the frequency of the fourth oscillator ( 43 ) is set so that the signal generator ( 22 ) at the injection frequency (ω _DUT + Δω) emitted wave (a ~ _{2_Δω} ) by means of the fourth mixer ( 42 ) is offset in the frequency position so as to fit in the passband width of the fourth filter ( 44 ) and she is the fourth detector ( 44 ) detected. Measuring device according to claim 19, characterized in that the first oscillator ( 34 ) and the fourth oscillator ( 43 ) are identical. Measuring device according to one of Claims 15 to 20, characterized in that in the second signal path ( 30 ) a fifth mixer ( 45 ), a fifth oscillator ( 46 ), a fifth filter ( 47 ) and a fifth detector ( 47 ), the frequency of the fifth oscillator ( 46 ) is set so that the at the signal generator ( 22 ) at a mirror frequency (ω _DUT - Δω) reflected wave (a ~ _{2_Δω} ) by means of the fifth mixer ( 45 ) is offset in the frequency position so as to fit into the passband width of the fifth filter ( 47 ) and she is the fifth detector ( 47 ) detected. Measuring device according to claim 21, characterized in that the second oscillator ( 37 ) and the fifth oscillator ( 46 ) are identical.

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