Band-pass microwave systems such as ultra-wideband antennas are traditionally characterized in the frequency-domain through a vector network analyzer in an anechoic chamber. A recent study proved antennas could be accurately measured in the time-domain using a step-function time-domain reflectometer (TDR), without the need for an anechoic chamber. We propose a new advance in the TDR characterization method. An impulse generator is employed in place of the step generator in a TDR set-up. The advantage conferred by this change is that more energy is available beyond a given frequency than with a step, and so a higher signal-to-noise ratio is achieved. The theoretical result is compared with measurement

McCabe, Steven Owen

Scott, Jonathan B.

IEEE Microwave and Wireless Components Letters

English

Name not available

Measurement of antennas and microwave components using time-domain reflectometry of a voltage impulse

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1Measurement of Antennas and MicrowaveComponents Using Time-Domain Reflectometry ofa Voltage ImpulseSteven McCabe, Student Member, IEEE, and Jonathan Scott, Senior Member, IEEEAbstract—Band-pass microwave systems such as ultra-wideband (UWB) antennas are traditionally characterized in thefrequency-domain through a vector network analyzer (VNA) inan anechoic chamber. A recent study proved antennas could beaccurately measured in the time-domain using a step-functiontime-domain reflectometer (TDR), without the need for ananechoic chamber. We propose a new advance in the TDRcharacterization method. An impulse generator is employed inplace of the step generator in a TDR set-up. The advantageconferred by this change is that more energy is available beyonda given frequency than with a step, and so a higher signal-to-noise ratio (SNR) is achieved. The theoretical result is comparedwith measurement.Index Terms—Antenna measurements, frequency-domain (FD)analysis, pulse measurements, time domain reflectometry (TDR),transient response.I. INTRODUCTIONT IME-DOMAIN reflectometry (TDR) is a well-knowntechnique in electronic and optical systems [1]–[4]. It hasrecently been used successfully in the characterization of an-tennas in [5] and [6]. The motivation behind this is twofold: ATDR is less costly than a vector network analyzer (VNA) [5],but more importantly the time-localization of the energy in thetest signal means that the user can dispense with the anechoicchamber that is required for antenna measurements with asinewave exciting signal.The traditional stimulus signal in a TDR is a voltage step.The energy in a step signal falls with increasing frequency. Inthe situation where the device under test (DUT) is interestingin only a limited high bandwidth, as with antennas, most ofthe energy of the step is wasted and the dynamic range of themeasurement is limited. On the other hand, an impulse testsignal has a theoretically flat bandwidth. In this paper, we ex-plore the advantages of making impulse TDR measurements,similar to a traditional TDR but employing an impulse-likesignal instead of a step-like signal. The work is timely becausea high-quality impulse generator has become available [7]–[9].This allows us to compare theory with measurement.II. FOURIER TRANSFORM OF THE STIMULUS SIGNALThe unit impulse (Dirac delta) function is defined as havingzero amplitude for all time except at t = 0, where it has infiniteamplitude:δ(t) ={0, t 6= 0∞, t = 0The Fourier transform for the unit impulse isF[δ(t)] = 1 (1)An ideal impulse has a flat frequency response. Although theunit impulse is a theoretical construct and does not physicallyexist [10], it is used as a limiting case when the width of apulse approaches zero. Derived from the convolution of tworectangular (“rect”) functions, the trapezoid function providesan approximation of a realistic impulse with finite rise and falltimes [11]:u(t) =1τrect(tτ)⊗A rect(tT)(2)where A is the trapezoid amplitude, T is the full width at halfmaximum (FWHM), and τ is the rise/fall time from 0 to 100%of the amplitude. The Fourier transform of u(t) is given byF[u(t)] = AT sinc(fτ) sinc(fT ) (3)The Heaviside unit step function is defined asH(t) = 1, t > 012 , t = 00, t < 0This function represents an ideal voltage step which is imme-diately elevated to a constant level at a definite time [12]. TheFourier transform of H(t) is given byF[H(t)] =1j2pif+12δ(f) (4)The response varies as the reciprocal of frequency and soapproaches zero amplitude as frequency tends to infinity.This theoretical construct does not physically exist becausea realistic step waveform has a finite rise time. The Fouriertransform for a step function s(t) with finite rise time is givenbyF[s(t)] =1j2pifsinc(fτ) (5)where τ is the rise time from 0 to 100% of the amplitude.Fig. 1 presents a number of spectra that will be compared2Fig. 1. The Fourier transforms of an ideal unit step, some practical step-like signals, and a practical trapezoidal pulse of unit amplitude. The unit formagnitude is dBV, namely the voltage relative to 1 Volt.with the spectrum of an ideal step (Heaviside unit step) thatappears as the dashed line. The new impulse source generatesimpulses with a typical FWHM of 23 ps [13]. The rise/falltime is estimated as 18 ps (5 ps flat-top). By inserting theseparameters in (3), the Fourier transform of a unit amplitudeimpulse was simulated in Matlab. This function can now becompared with the unit step from (4) and some realistic stepwaveforms from (5) in Fig. 1. It can be seen that even therealistic, limited impulse signal contains more energy thanan ideal step for frequencies above about 7.5 GHz. When thestep waveform is not ideal, but similar to what is practicallyavailable today, the comparison becomes even more favorable,as can be seen in the same figure.III. MEASURED RESULTSAn impulse-style TDR was constructed as shown in Fig. 2.The set-up features an impulse generator with a 23 ps pulsewidth [7]–[9], a DC to 26.5 GHz power divider, and an18 GHz TDR operating in oscilloscope mode [14]. The DUTwas a Wide-Band sector antenna designed to operate between5.47-5.85 GHz. A step-type TDR set-up was constructed usinga similar configuration but with the impulse source replacedwith a 50Ω dummy load and the mainframe set in TDRmode. The divider was included to replicate the conditionsof the impulse TDR set-up so that fair comparisons betweentechniques could be made. An attenuator was also insertedbetween the oscilloscope channel and the divider, to furtherreduce the step signal to a similar amplitude produced in theimpulse TDR set-up. Calibrated measurements were acquiredusing a VNA, where the DUT was situated outdoors toprovide an accurate reference for comparison with the TDRmeasurements.A. Acquisition in the Time-DomainTwo time-domain measurements were employed in the sub-sequent frequency-domain processing: A reference waveformreflected from a short, and the waveform reflected by theantenna. Averaged measurements taken by the impulse TDRset-up were windowed with the Dirichlet window in Matlab,to remove the incident portion of the signal and to removespurious reflections as required for subsequent frequency-domain processing as reported in [5]. The rectangular windowcontained the essential data that corresponded to the DUTRF source Impulse generator TDR1TrigPower divider DUTFig. 2. An impulse TDR set-up for the measurement of microwave devices.A generated impulse is transferred to the DUT, resulting in a reflection thatis monitored on the TDR. The dashed line represents the reference plane atthe DUT connector.Fig. 3. Comparison of |S11(f)| dB measurements made by the impulseTDR, step TDR, and VNA, limited to the working frequency range of thewide-band antenna. The superior dynamic range of the VNA is evident wherethe magnitude drops to almost −30 dB.response, and provided a reference plane extended to the endof the cable where the DUT was to be attached. The length ofthe time window was chosen so that there was sufficient timefor the antenna’s reflection to settle, while limited to blockout spurious reflections caused by the presence of objects nearthe antenna. Initially, a 35 ns acquisition window was chosenas endorsed in [5]. The same process was followed for theacquisition of the step TDR measurements.B. Transformation to the Frequency-DomainThe zero-padding operation was employed to ensure ade-quate frequency resolution, along with the application of theNicolson algorithm to avoid truncation error [3]. A computerprogram computed the discrete Fourier transform (DFT) forboth the reference reflection and DUT reflection, resultingin Vref (f) and VDUT (f). The reflection scattering parameterS11(f) was then computed by S11(f) = VDUT (f)/Vref (f)for frequencies between 2.0-9.0 GHz. The DUT |S11(f)| dBresponse obtained by both the impulse TDR and step TDRmethods, were plotted against the VNA reference as shownin Fig. 3. The frequency range shown is constrained to theantenna’s specified operating range.C. VarianceA plot of the |S11(f)| variance measured between the TDRmeasurements and the VNA reference are shown in Fig. 4.3Fig. 4. |S11(f)| variance measured to 9GHz between each TDR systemresponse and the VNA reference.Fig. 5. The frequency spectra for the impulse TDR and step TDRmeasurements when the (a) reference short was connected at the referenceplane (b) DUT was connected at the reference plane. The noise floor wasdetermined by measuring the noise present in the system with the signalsource disabled.The frequency axis is limited to the 9.0 GHz bandwidth of theVNA. The impulse TDR measurement clearly contains lessvariance than the step TDR measurement, especially above7.0 GHz.D. Dynamic RangeThe spectra measured in the reference short reflections forboth the impulse TDR and step TDR systems are shown inFig. 5(a). Similarly, the spectra present in the DUT reflectionfor each TDR set-up are shown in Fig. 5(b). It is apparent fromboth figures that the energy in the impulse TDR reflectionexceeds the energy in the step TDR reflection above about3.1 GHz. Beyond 3.1 GHz the 23 ps impulse TDR offers asignificant improvement in SNR compared with the Agilent54754A 40 ps step TDR. Recommendations for the appli-cation of impulse TDR, step TDR, and VNA measurementtechniques, are summarized in Table I. The numerical valuefor each parameter will vary with circumstance and so onlytrends are given.TABLE ICOMPARISON OF MEASUREMENT TECHNIQUESTechnique Bandwidth Dynamic Equipment Anechoic(GHz) range cost chamberImpulse TDR Med Med Med NoStep TDR Low Low Med NoVNA High High High YesIV. CONCLUSIONIn the situation where the user will post-process reflectionwaveform data, for example, to determine S-parameters, theimpulse version of TDR is superior at frequencies above7 GHz. It may also be advantageous when the user is lookingfor precision in spatial localization, say in a connector orsimilar in-line structure, as the increased energy at higherfrequencies can help.ACKNOWLEDGEMENTThe authors wish to acknowledge the support of AgilentTechnologies Component Test Division for the supply anddetailed support of equipment. Thanks are also due to SkynetData Communications Technology Ltd for the supply of equip-ment and support.REFERENCES[1] C. Chiu, W. Chen, K. Liao, B. Chen, Y. Teng, G. Huang, and L.Wu, “Pad characterization for CMOS technology using time domainreflectometry”, in Proc. IEEE Int. RF and Microwave Conf., in KualaLumpur, Dec. 2008, pp. 215-217.[2] M. Harper, N. Ridler, and M. Salter, “Comparison between root-impulse-energy and vector network analyzer methods for measuring loss onprinted circuit boards”, in ARFTG Microwave Measurement Symp., inPortland, OR, 2008, pp. 20-25.[3] A. Cataldo, L. Catarinucci, L. Tarricone , F. Attivissimo, and A. Trotta,“A TD-FD combined method for enhancing reflectometry measurementsin liquid quality monitoring”, in Proc. IEEE Instrum. Meas. Tech. Conf.,in Warsaw, May. 2007, pp. 1-5.[4] M. Gerding, T. Musch, and B. Schiek, “A novel approach for a high-precision multitarget-level measurement system based on time-domainreflectometry” IEEE Tran. Microw. Theory Tech., vol. 54, no. 6, pp.2768-2773, Jun. 2006.[5] A. Cataldo, G. Monti, E. De Benedetto, and G. Cannazza, L. Tarricone,and L. Catarinucci, “Assessment of a TD-based method for character-ization of antennas”, IEEE Trans. Instrum. Meas., vol. 58, no. 5, pp.1412-1419, May. 2009.[6] R. Tamas, G. Caruntu, and D. Popa, “A time-domain measuring tech-nique for ultra-wide band antennas”, Microwave and Optical TechnologyLetters, vol. 53, no. 2, pp. 281-286, Feb. 2011.[7] J. Scott and D. Gunyan, “Pulse generator”, US patent number 7,423,470,Sep, 2008.[8] J. Scott and M. Hoy, “Group-delay measurement of frequency-converting devices using a comb generator”, IEEE Trans. Instrum.Meas., vol. 59, no. 11, pp. 3012-3017, Nov. 2010.[9] P. Blockley, D. Gunyan, and J. Scott, “Mixer-based, vector-corrected,vector/network analyzer offering 300kHz-20GHz bandwidth and trace-able response”, IEEE Int. Microwave Symp. in Long Beach, CA, Jun.2005, pp. 1-4.[10] S. Haykin and M. Moher, Introduction to analog & digital communica-tions, second edition, John Wiley & Sons, Inc, pp. 42-49, 2007.[11] D. Brandwood, Fourier transforms in radar and signal processing,Artech House, Inc., pp. 39-47, 2003.[12] R. N. Bracewell, The fourier transform and its applications, thirdedition, McGraw-Hill International Editions, pp. 61, 2000.[13] Agilent U9391C/F comb generators technical overview, AgilentTechnologies, [Online]. Available: http://www.home.agilent.com/agilent/product.jspx?pn=U9391C retrieved Jan 2010.[14] Agilent 54753A and 54754A TDR plug-in modules user guide, AgilentTechnologies, publication number 54753-97015, 2000.

A novel approach for a highprecision multitarget-level measurement system based on time-domain reﬂectometry”

A TD-FD combined method for enhancing reﬂectometry measurements in liquid quality monitoring”, in

A time-domain measuring technique for ultra-wide band antennas”,

Agilent 54753A and 54754A TDR plug-in modules user guide, Agilent Technologies, publication number 54753-97015,

Agilent U9391C/F comb generators technical overview,

Assessment of a TD-based method for characterization of antennas”,

Comparison between root-impulseenergy and vector network analyzer methods for measuring loss on printed circuit boards”,

Fourier transforms in radar and signal processing,

Group-delay measurement of frequencyconverting devices using a comb generator”,

Introduction to analog & digital communications, second edition,

Mixer-based, vector-corrected, vector/network analyzer offering 300kHz-20GHz bandwidth and traceable response”,

Pad characterization for CMOS technology using time domain reﬂectometry”, in

Pulse generator”, US patent number 7,423,470,

The fourier transform and its applications, third edition,

Measurement of antennas and microwave components using time-domain reflectometry of a voltage impulse

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