ARL-TN-0783 ● SEP 2016

US Army Research Laboratory

Conversion of Radio-Frequency Pulses to 

Continuous-Wave Sinusoids by Fast Switching 

and Narrowband Filtering

by Gregory J Mazzaro, Andrew J Sherbondy,

Kenneth I Ranney, and Kelly D Sherbondy

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ARL-TN-0783 ● SEP 2016

US Army Research Laboratory

Conversion of Radio-Frequency Pulses to 

Continuous-Wave Sinusoids by Fast Switching 

and Narrowband Filtering

by Gregory J Mazzaro, Andrew J Sherbondy,

Kenneth I Ranney, and Kelly D Sherbondy

Sensors and Electron Devices Directorate, ARL

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1. REPORT DATE (DD-MM-YYYY)

September 2016

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Technical Note

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07/2016–08/2016

4. TITLE AND SUBTITLE

Conversion of Radio-Frequency Pulses to Continuous-Wave Sinusoids by Fast 

Switching and Narrowband Filtering

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Gregory J Mazzaro, Andrew J Sherbondy, Kenneth I Ranney, and 

Kelly D Sherbondy

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US Army Research Laboratory

ATTN: RDRL-SER-U

2800 Powder Mill Road

Adelphi, MD 20783-1138

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ARL-TN-0783

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The authors seek to reduce self-generated distortion in the transmitted probe of an intermodulation radar by applying 

Linearization by Time-Multiplexed Spectrum (LITMUS). In this technical note, an experiment is conducted to select a 

minimum time-multiplexing rate and an appropriate filter to accomplish LITMUS when transmitting cellular-band frequencies. 

This research will be followed by a wireless experiment that demonstrates an improvement in the linearity of a short-range 

intermodulation radar.

15. SUBJECT TERMS

distortion, filter, intermodulation, linearization, radar, radio frequency, self-generated, time multiplexing, transmitter

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Kenneth I Ranney

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(301) 394-0832

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iii

Contents

List of Figures iv

1. Introduction 1

2. Experiment 2

3. Conclusions 10

4. References 11

Appendix. Network Parameters 13

Distribution List 15
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iv

List of Figures

Fig. 1 Switch-and-filter experiment: equipment and arrangement ..................2

Fig. 2 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 5 

MHz. The output of the ZX75BP-942 filter is essentially the same as the 

RF pulse input. The output of the ZVBP-909 filter contains significant 

amplitude modulation. ...........................................................................4

Fig. 3 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz 

and fs = 5 MHz.....................................................................................5

Fig. 4 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 

10 MHz. The output of the ZX75BP-942 filter is essentially the same as 

the RF pulse input. The output of the ZVBP-909 filter contains less 

amplitude modulation compared to fs = 5 MHz.....................................6

Fig. 5 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz 

and fs = 10 MHz...................................................................................7

Fig. 6 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 

20 MHz. The output of the ZX75BP-942 filter is essentially the same as 

the RF pulse input. The output of the ZVBP-909 filter is a 

constant-amplitude, continuous sinusoid...............................................8

Fig. 7 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz 

and fs = 20 MHz...................................................................................9

Fig. A-1 Two-port network parameters for the MiniCircuits filters used in this 

experiment. S11 and S21 were measured using the Keysight N5242A 

with 0 dBm output from Port 1............................................................14
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1

1. Introduction

One challenge of designing a nonlinear radar is to achieve linearity in the 

transmitter that is high enough to detect targets whose reflections are typically very 

weak. The generation of a detectable nonlinear target response at a practical 

standoff range generally requires transmission of at least 30 dBm of average radio

frequency (RF) power.1 At the target, the loss incurred by the conversion of 

incident power at a set of transmit frequencies into reflected power at a different set 

of received frequencies and is often greater than 30 dB.2 Therefore, the radar 

receiver’s sensitivity must be relatively high to detect a nonlinear target.

Generating high power for transmission is achieved at the cost of linearity. At the 

output of a typical RF amplifier, for every 1 dB of additional peak power 

transmitted at the pair of frequencies, f1 and f2 , the power at the (undesired, 

spurious) third-order intermodulation frequencies, 2f1 – f2 and 2f2 – f1 increases by 

3 dB.3 If these self-generated spurious frequencies are not attenuated or otherwise 

eliminated before they arrive at the transmit antenna they will, a) couple directly 

from the transmitter to the receiver, or b) radiate into the environment and reflect 

from purely linear targets and/or clutter. Coupling from a high-power transmitter to 

a sensitive receiver tends to saturate the receiver such that no targets may be 

detected. Nonlinear reflections from linear targets and clutter manifest as 

false-alarm detections.

An intermodulation radar relies on the target to respond at one or more frequencies 

produced by the mixing of transmit frequencies that are simultaneously present in 

the target.4–7 The same nonlinear electrical properties that produce harmonics at 

integer multiples of a single transmit frequency produce intermodulation 

frequencies at integer sums and differences of multiple transmit frequencies (e.g.,

3f2 – 2f1, 3f1 – 2f2). Since these multiple transmit frequencies are usually closely 

spaced (i.e., because many antennas are designed to operate within a particular 

communications band), intermodulation frequencies are also closely spaced and 

appear very near to the original transmit frequencies. Filtering is rarely 

implemented to eliminate self-generated intermodulation as such filters must be 

very narrow and are thus prohibitively lossy. Common techniques used to improve 

linearity (i.e., linearize) in this case are predistortion8 and feed-forward 

cancellation.

9

Another distortion-mitigation technique, yet to be implemented as part of a 

nonlinear radar, is Linearization by Time-Multiplexed Spectrum (LITMUS).10 The 

LITMUS technique reduces distortion introduced by a nonlinear element in an RF 

front-end (i.e., a power amplifier) by time-multiplexing an otherwise frequency-or 
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phase-multiplexed signal before the nonlinear element, passing the 

time-multiplexed version of the signal through the nonlinear element (at a lower 

peak power, but at the same total power as the non-multiplexed version), and 

reversing the time-multiplexing operation by attaching a carefully selected filter to 

the output of the nonlinear element. Linearity is improved at the cost of a slight 

increase in complexity in the RF chain and a spreading of the transmit signal’s 

bandwidth immediately before the signal encounters the nonlinear element. In 

previous work, a reduction by 14 dB in third-order intermodulation was 

demonstrated for the generation of 4 mW of average power in 4 tones by an RF 

amplifier.11 In this technical note, an appropriate filter and a minimum 

time-multiplexing rate are selected to apply LITMUS to intermodulation radar.

12

2. Experiment

To apply LITMUS to the transmission of multiple evenly spaced equal-amplitude 

frequencies (that will ultimately be used to illuminate a nonlinear target 

simultaneously), 2 subsystems of the RF chain are paramount: a) the 

time-multiplexer, which is illustrated in Fig. 1 as a rotary switch; and b) the filter, 

which is labeled in Fig. 1 as “BPF” for bandpass filter. As explained in Mazzaro et 

al.,

12 the time-multiplexer must be able to chip the signal spectrum at a rate that is 

significantly greater than the bandwidth of the filter. Also, the filter must have a 

passband whose width is smaller than the chip rate, and it must have a stopband that 

eliminates (or significantly attenuates) all spectral products introduced by the 

time-multiplexer.

Fig. 1 Switch-and-filter experiment: equipment and arrangement

An experiment was designed to convert a single-tone RF pulse with a carrier 

frequency in the vicinity of 900 MHz1 into a constant-amplitude (i.e., “always on” 

or “continuous”) sinusoid at that same carrier frequency. The same process that

converts an RF pulse into a sinusoid will convert a switched-tone signal containing 

multiple frequencies into a steady multitone signal.

11 Thus, a switching rate and a 

filter that achieve the conversion for one frequency can be used as the initial design
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parameters of a wireless experiment to demonstrate the application of LITMUS to 

an intermodulation radar that transmits multiple frequencies.

For the experiment, a constant-envelope (3 dBm) single-frequency sinusoid is 

generated by the Agilent N9310A RF signal generator. Time-multiplexing is 

achieved by enabling in-phase/quadrature (I/Q) modulation on the N9310A and 

routing 1-V/0-V 50% duty-cycle pulses from the Agilent 33220A function 

generator to the in-phase port on the N9310A. (The quadrature port was grounded.) 

Essentially, the on/off signal provided by the 33220A modulated the carrier that 

was provided by the N9310A. The resulting RF pulses output from the N9310A 

were sent directly to a bandpass filter. In the follow-on experiment, the RF pulses 

will be sent through an amplifier (i.e., the “nonlinear element” in Fig. 1) to generate 

a high-power/high-linearity radar probe.

12

The following bandpass filters were tested: MiniCircuits ZX75BP-942+ and 

MiniCircuits ZVBP-909+. The following carrier frequencies were tested: f0 = 900 

MHz to 920 MHz in 1-MHz steps. These center frequencies were chosen to stay 

within the passband of both filters, as required by LITMUS.12 The following 

switching frequencies were tested: fs = 5 MHz, 10 MHz, 20 MHz. These switching 

frequencies represent 3 of the highest time-multiplexing rates possible with the 

33220A. The input to and output from each bandpass filter, for all frequency 

combinations, was captured by the Lecroy Wavemaster 8300A digitizing 

oscilloscope at 10 GSa/s. Figures 2–7 contain samples of the recorded data.

Figure 2 shows vin and vout from the 2 filters for f0 = 908 MHz and fs = 5 MHz. As 

observed, the switching frequency is sufficient to change the shape of the RF pulse 

as it propagates through the ZVBP-909; however, it is not high enough to change 

the shape of the RF pulse as it propagates through the ZX75BP-942. The shaping 

(or lack thereof) of the RF pulse from vin to vout may also be viewed in the frequency 

domain. Power spectra are provided in Fig. 3: Pin is average power corresponding 

to the voltage vin delivered into a 50-Ω impedance; each Pout corresponds to each

vout. The closer a power spectrum resembles a single peak in the frequency domain, 

the closer the waveform resembles a sinusoid in the time domain. The ZVBP-909 

filters the wide spectrum of the sharp RF pulse into a small subset (i.e., essentially 

5) of its original Fourier components. The passband of the ZX75BP-942 is too wide 

to have a significant effect on the RF pulse; its Pout is nearly the same as Pin. 

(S-parameters for the 2 filters are provided in the Appendix.)
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Fig. 2 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 5 MHz. The 

output of the ZX75BP-942 filter is essentially the same as the RF pulse input. The output of 

the ZVBP-909 filter contains significant amplitude modulation.
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Fig. 3 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz and 

fs = 5 MHz

Figure 4 shows vin and vout for fs = 10 MHz, and Fig. 5 shows the corresponding 

power spectra. Here, only 3 Fourier components are visible at the output of the 

ZVBP-909. Thus the time-domain waveform more closely resembles a 

single-frequency sinusoid. Significant amplitude modulation of the sinusoid is still 

evident, however.
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Fig. 4 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 10 MHz. The 

output of the ZX75BP-942 filter is essentially the same as the RF pulse input. The output of 

the ZVBP-909 filter contains less amplitude modulation compared to fs = 5 MHz.
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Fig. 5 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz and

fs = 10 MHz

Figure 6 shows vin and vout for fs = 20 MHz, and Fig. 7 shows the corresponding 

power spectra. At this switching frequency, only a single Fourier component at 

908 MHz is observable at the output of the ZVBP-909 filter, and correspondingly 

the time-domain waveform is a constant-amplitude, continuous sinusoid. For this 

particular filter, this particular switching frequency, and this particular carrier 

frequency, the original RF pulse waveform has been converted to a continuous 

sinusoid. The experiment is judged successful, and this combination of filter and 

frequencies will be used as the starting point for the next phase of this research, 

which is to apply the switching-and-filtering LITMUS technique to 

intermodulation radar.
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Fig. 6 Switch-and-filter experiment: time-domain data for f0 = 908 MHz, fs = 20 MHz. The 

output of the ZX75BP-942 filter is essentially the same as the RF pulse input. The output of 

the ZVBP-909 filter is a constant-amplitude, continuous sinusoid.
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Fig. 7 Switch-and-filter experiment: frequency-domain data for f0 = 908 MHz and

fs = 20 MHz
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3. Conclusions

An experiment was performed to select a time-multiplexing rate and filter 

appropriate to apply LITMUS to intermodulation radar. The parameters tested were 

the following: a) carrier frequencies in the vicinity of 900 MHz, b) switching rates 

up to 20 MHz, and c) filters with passbands in the vicinity of 900 MHz. A test that

successfully converted a single-frequency square-pulse train into a 

constant-amplitude and continuous-wave sinusoid was conducted at a carrier 

frequency of 908 MHz, a switching frequency of 20 MHz, and a bandpass filter 

centered at 909 MHz with a passband of 13 MHz. These parameters will guide the 

development of a follow-on experiment to detect nonlinear targets using a 

multitone probe with linearity improved by LITMUS.
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4. References

1. Mazzaro GJ, Martone AF, McNamara DM. Detection of RF electronics by 

multitone harmonic radar. IEEE Transactions on Aerospace and Electronic 

Systems. Jan. 2014;50(1):477–490.

2. Dardari D. Detection and accurate localization of harmonic chipless tags.

EURASIP Journal on Advances in Signal Processing. 2015;2015(1):1–13.

3. Pedro JC, Carvalho NB. Intermodulation distortion in microwave and wireless 

circuits. Boston, MA: Artech House, 2003.

4. Vernigorov NS, Borisov AR, Kharin VB. Application of the multifrequency 

signal in a nonlinear radar. Journal of Communications Technology and 

Electronics. Nov. 1998;43(1)59–62.

5. Martone AF, Delp EJ. Characterization of RF devices using two-tone probe 

signals. IEEE/SP 14th Workshop on Statistical Signal Processing, pp. 

161–165, Aug. 2007.

6. Viikari V, Kantanen M, Varpula T, Lamminen A, Alastalo A, Mattila T, 

Seppa H, Pursula P, Saebboe J, Cheng S, Al-Nuaimi M, Hallbjorner P, 

Rydberg A. Technical solutions for automotive intermodulation radar for 

detecting vulnerable road users. Proceedings of the IEEE 69th Vehicular 

Technology Conference (VTC), pp. 1–5, Apr. 2009.

7. Saebboe J, Viikari V, Varpula T, Seppa H, Cheng S, Al-Nuaimi M, 

Hallbjorner P, Rydberg A. Harmonic automotive radar for VRU classification.

Proceedings of the International Radar Conference (RADAR), pp. 1–5, 

Oct. 2009.

8. Helaoui M, Boumaiza S, Ghazel A, Ghannouchi FM. Power and efficiency 

enhancement of 3G multicarrier amplifiers using digital signal processing with 

experimental validation. IEEE Transactions on Microwave Theory and

Techniques. Apr. 2006;54(4)1396–1404.

9. Wetherington JM, Steer MB. Robust analog canceller for high-dynamic-range 

radio frequency measurement. IEEE Transactions on Microwave Theory and 

Techniques. June 2012;60(6):1709–1719.

10. Mazzaro GJ, Gard KG, Steer MB. Linear amplification by time-multiplexed 

spectrum. IET Circuits, Devices, and Systems. Sept. 2010;4(5):392–402.
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11. Mazzaro GJ, Gard KG, Steer MB. Low distortion amplification of multisine 

signals using a time-frequency technique. IEEE MTT-S International 

Microwave Symposium Digest, pp. 901–904, June 2009.

12. Mazzaro GJ, Sherbondy AJ, Ranney KI, Sherbondy KD. Linearizing an 

intermodulation radar transmitter by filtering switched tones. In preparation 

for the proceedings of SPIE Defense and Commercial Sensing 2017, Anaheim, 

CA, Apr. 2017.
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Appendix. Network Parameters
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The network parameters S11 and S21 for the MiniCircuits ZX75BP-942+ and 

MiniCircuits ZVBP-909+ filters were recorded using the Keysight N5242A 

nonlinear network analyzer. The magnitude (in decibels) of each 2-port parameter 

is shown in Fig. A-1.

Fig. A-1 Two-port network parameters for the MiniCircuits filters used in this experiment.

S11 and S21 were measured using the Keysight N5242A with 0-dBm output from Port 1.
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