Study of Pulsed RF Signal Extraction and Irradiation from a Capacitive Nonlinear Transmission Line

Research on Nonlinear Transmission Lines (NLTLs) has long been carried out to produce oscillating pulses. The radiofrequency (RF) pulses generated by the NLTLs can be radiated by antennas connected to the output of the lines. Possible applications of NLTLs as an RF generator include aerospace radars, telecommunications, battlefield communication disruption, and medical devices. There have been relatively few articles that presented experimental results regarding the extraction and the radiation of the RF signal from NLTLs. This article reports the excellent results obtained with a low voltage lumped capacitive NLTL in which oscillations of the order of 230 MHz were produced and radiated using Double-Ridged Guide (DRG) antennas. The RF signal was extracted using a decoupling circuit based on a Chebyshev high-pass filter. The NLTL was evaluated through time domain and frequency domain analyses of the pulsed RF signal measured on a resistive load connected to the output of the line, as well as on transmitting and receiving by antennas. The LT-SPICE model of the line was implemented and the comparison of simulation and experimental results presented a good agreement.


I. INTRODUCTION
Recently, the NLTL technology has been studied to produce high power microwave signals. The NLTLs can be used as an alternative technique for pulsed high-power transmitters that includes the RF generator and the solid state (SSA) / traveling wave tube (TWT) amplifiers [1,2]. High power pulses with a peak power of 20 MW have been produced in the frequency range of 1 GHz [3]. In [4], a capacitive NLTL produced a peak power of 60 MW at 200 MHz. Other works presented the development of high power NLTLs for medical applications [5,6]. They are studying the physiological responses of pulsed RF signal focusing on cancer treatment. Another study demonstrated the design of Radiofrequency Identification (RFID) system based on NLTL [7]. RFID uses electromagnetic fields to identify and track tags attached to objects. It is often seen as an important component of the Internet of Things (IoT) [8]. The high power NLTL could be used as a transmitter section of aerospace radars that includes the pulse modulator and the high power amplifier. In a pulsed radar, the transmitted RF pulsed signal reflects from a surface of an object and returns to a receiver giving information about the location and the speed of the object. Signal processing of this information can be used to create a high-resolution image of the object. This technology is used in Synthetic Aperture Radar (SAR) [9]. A recent article presented the advances that have enabled CubeSats as viable platforms for radar missions. However, the size and weight constraints of the CubeSat drive many of the radar RF design challenges [10]. Considering that the NLTLs used as a pulsed RF transmitter offer advantages such as simplicity , lightweight, compactness and lower cost, this technology can be seen as a promising alternative for space missions involving nanosatellites. Very few articles presented experimental results regarding the transmission and reception of the RF signals generated by lumped capacitive NLTLs. Although most of the studies are concentrated on high voltage NLTL, an experiment with low voltage has the advantage that the NLTL can be assembled with commercial-off-the-shelf (COTS) components and the measurements can be performed with good accuracy in the laboratory. This kind of experiment is important to evaluate the soliton propagation characteristics such as time delay, width, number of oscillations and voltage modulation depth (VMD). Previous works investigated the performance of low voltage capacitive NLTLs. They analyzed the nonlinear partial differential equation (PDE) of these networks, the influence of the input pulse shape and the resistive load on the RF generation [11][12][13]. This paper reports an investigation of the performance of a 20-section lumped capacitive NLTL based on varactor diodes. In this work, the line was driven by a 13 V input signal with a frequency repetition rate of 5 MHz to produce a pulsed RF signal with oscillations of voltage modulation depth (VMD) of about 5 V and frequency around 230 MHz. The pulsed signal generated by the NLTL was first measured on a resistive load. Then a Chebyshev filter was designed and connected to the line output to extract only the high-frequency spectral components of the signal. The output signal was radiated and received using two double-ridge guide antennas. The NLTL performance was evaluated through time domain analysis and Fast Fourier transform (FFT) of the RF signal. An LT-SPICE model of this line was used for comparison between simulations results and experimental data.

II. NLTL BASIC THEORY
A capacitive NLTL is implemented using inductors and variable capacitors as nonlinear components arranged in a series of LC section low pass filters (Fig.1). In this experiment, a varactor diode is used as a variable capacitor (Fig. 1). The capacitance of the diode varies according to the applied reverse voltage. The input pulse injected into the line propagates down the line length. As the capacitance of the varactor diodes decreases with the pulse amplitude, the portion of the pulse with higher amplitude will travel faster than its part with lower amplitude. It happens because the propagation velocity of the pulse increases as the voltage increases. In this case, the soliton wave formed by the higher voltage overtakes the wave produced by the lower voltage, and then the oscillating soliton is formed in the final section of the line. The phase velocity can be calculated using [14] where C(V) is the variable capacitance as a function of the voltage applied across the varactor diode and L is the inductance.
The cutoff frequency of the line, known as the Bragg frequency, is given by [14] f c = 1 π√LC(V max ) ⁄ where C(Vmax) is the capacitance at the maximu m voltage applied across the varactor diode. Another important parameter of the line is the characteristic impedance [14] The impedance of the line also depends on the reverse voltage applied on the diode varactor. As reported before the diode capacitance decreases with the voltage.

III. EXPERIMENTAL AND SIMULATION RESULTS
The measurements were performed on a 20-section capacitive NLTL that was built with linear inductors of 100 nH and SVC236 varactor diodes (Fig. 2). The SVC236 diode capacitance-voltage behavior obtained from the manufacturer's datasheet [15] is shown in Fig. 3. is of about 11.5 pF, which gives 93% of capacitance change from the unbiased value to the capacitance value at 10 V. Since the NLTL never fully matches the load as the line characteristic impedance according to (3)

RESISTIVE LOAD MEASUREMENTS
The measurements were evaluated from the signal measured through the 50 Ω input of the oscilloscope. A 30 dB attenuator was connected between the line output and the oscilloscope input (Figs. 6 and 7).  The time response of the simulation and experimental measurement at the 50 Ω resistive load, according to the test setup shown in Fig. 6, is presented in Fig. 8 in short-time and long-time scales to show the pulse repetition frequency of 5 MHz.

: Time domain plots of the input pulse (experimental) and the waveforms obtained on the 50 Ω resistive load (simulation and measurement) in a short-time scale (a) and in a long-time scale (b).
The frequency domain plot on the decibel scale is shown in Fig. 9. The frequency of the oscillations obtained from measurement and simulation is around 230 MHz.

International Journal of Advanced Engineering Research and Science (IJAERS)
[  Fig. 9, frequency component around 230 MHz was generated by the capacitive NLTL. In order to separate this frequency from the low voltage components of the input pulse signal, a high-pass filter with a cutoff frequency of 200 MHz was designed and connected at the output of the line. A third-order Chebyshev high-pass filter with T topology was chosen for this experiment. The Chebyshev response has ripples in the passband. For this experiment, 0.25 dB ripple was chosen as a designed parameter. Considering the line impedance equal to load impedance, the element values (C1', L' and C2') for a normalized Chebyshev filter with 0.25 dB ripple are 1.3034, 1.1463 and 1.3034, respectively [16]. The filter components were calculated according to [17,18]  The circuit was implemented using a commercial standard capacitor and inductor values (Fig. 10). The filter was constructed in a separated circuit board to be characterized before the connection with the line (Fig. 11). For insertion loss calculation the filter circuit is represented by impedances (Fig. 12). ://dx.doi.org/10.22161/ijaers.5.10.17  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 127 Fig. 12: Open-circuit impedances structure.

International Journal of Advanced Engineering Research and Science (IJAERS) [Vol-5, Issue-10, Oct-2018] https
The network between port 1 and port 2 can be represented with the ABCD matrix as: The impedances Za, Zb, and Zc can be calculated by where C1=C2=13 pF, L=35 nH and ω = 2πf.
Then the elements of the ABCD matrix were calculated below = 1 + ⁄ (10) The relation between the input voltage (V1) and current (I1) and output voltage (V2) and current (I2) of a two-port network (Fig. 13) can be represented as: where A, B, C, and D coefficients are frequency dependent. Fig. 13: Two-port network.
The transfer function VS/VL for the circuit in Fig. 13 is given by where VS and VL are the source and load voltages, respectively, and ZS and ZL are source and load impedances, respectively.
Then, using (7)-(9), (10)- (13), and the ratio VS/VL given by (15), the insertion loss function can be calculated by where P1 is the power delivered to the load when the network is removed from the circuit whereas P2 is the power delivered to the load when the network is in place.
Finally, the insertion loss (IL) of the filter can be expressed in dB: Considering ZS = ZL= 50 Ω the insertion loss was calculated and measured through a Vector Network Analyzer (VNA) for the frequency range between 10 MHz and 500 MHz (Fig. 14).

International Journal of Advanced Engineering Research and Science (IJAERS)
[Vol-5, Issue-10, Oct-2018] https: //dx.doi.org/10.22161/ijaers.5.10.17  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Page | 128 According to Fig. 14 the calculated insertion loss presents a good agreement with the measurement results. The high-pass filter was connected to the output of the capacitive NLTL. The measurements were evaluated from the signal measured through the 50 Ω input of the oscilloscope (Fig. 15). The time response of the simulation and experimental measurement at the NLTL connected to a 50 Ω load through a high-pass filter, according to the test setup shown in Fig. 15, is presented in Fig. 16 in short-time and long-time scales. The frequency domain plot on the decibel scale is shown in Fig. 17.    18 shows the comparison between the measurements of the RF pulsed signal at the output of the line without the highpass filter (Fig. 9) and with the high-pass filter (Fig. 17). It is possible to see that the filter provided a high attenuation for the low-frequency components.

International Journal of Advanced Engineering Research and Science (IJAERS)
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IV. RADIATION MEAS UREMENTS
Two Double-Ridged Guide (DRG) antennas (ETS-Lindgren 3106B) were used to transmit and receive the RF signal. It is a broadband antenna that operates in the frequency band from 200 MHz up to 1 GHz. The antennas were placed in vertical polarization with a two -meter spacing. The receiving antenna terminal was connected through a coaxial cable to the 50 Ω input of the oscilloscope. The measurements were performed in an anechoic chamber to avoid electromagnetic interference (Figs. 19 and 20).    23 shows the comparison between the RF pulsed signal at the output of the line without the high-pass filter (Fig. 9), with the high-pass filter (Fig. 17) and received by the DRG antenna (Fig. 22). V. CONCLUSION This article reports the excellent results obtained with a 20section low voltage lumped capacitive NLTL in which oscillations of the order of 230 MHz were produced and radiated using Double-Ridged Guide (DRG) antennas. The performance of the line was investigated focusing on the extracting of the RF signal from the line and the irradiation by an antenna. The LT-SPICE models implemented for simulations presented a good agreement with the experimental data.