SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit

applied sciences

Article SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit

Yong-Hyeok Lee 1 , Sung-yong Cho 2 and Jae-Young Chung 1,*

1 Department of Electrical and Information Engineering; SeoulTech, Seoul 01811, Korea; [email protected] 2 Department of Manufacturing Systems and Design Engineering; SeoulTech, Seoul 01811, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-2-970-6445

Received: 2 June 2020; Accepted: 24 June 2020; Published: 28 June 2020

Featured Application: Miniaturized broadband antennas for wireless communication devices

Abstract: A non-Foster circuit (NFC) is known as an active broadband matching technique to improve the impedance matching bandwidth of an electrically small antenna (ESA). There has been a vast amount of papers that report the generation of negative impedance using an NFC and its eﬀectiveness on broadband antenna matching. However, only a few discussed its impact on the signal-to-noise-ratio (SNR), which is one of the most important ﬁgures-of-merit for a wireless communication system. In this paper, the SNR enhancement due to an NFC was measured and discussed. An NFC was carefully designed to have a low dissipation loss and to meet the stability conditions. The optimized NFC design was fabricated and applied to an ESA length of λ⁄15 at a frequency range of 150 to 300 MHz. The measured results showed that the NFC enhanced the received power of the antenna system by more than 17 dB. However, due to the noise added by the NFC, the SNR enhancement was not guaranteed for some frequency points. Nevertheless, an average of 7.3 dB of SNR improvement over the frequency band of interest is possible based on the experiment result.

Keywords: broadband impedance matching; electrically small antenna; non-Foster circuit; UHF; VHF

1. Introduction The demand for miniaturized communication systems has tremendously increased for many applications such as mobile devices, medical wearables, military radios and vehicles, etc. One of the key components that prohibit the miniaturization is an antenna because of its physical length (or area) requirement, depending on the frequency. For example, the ideal length of a quarter-wavelength antenna operating at 300 MHz is 25 cm. No matter how small the design of the circuit or chassis is, the size of the whole communication system is big due to the antenna. For the last decade, a vast amount of research has been conducted on the so-called electrically small antenna (ESA), which is deﬁned by an antenna whose maximum dimension is less than λ/2π [1,2]. Although an ESA presents a small footprint, it usually accompanies low radiation resistance and high reactance, which makes it diﬃcult to match to the system impedance (e.g., 50 Ω). To promote the impedance matching, often passive components, such as inductors (L) and capacitors (C), are used to remove the reactance at a designated frequency band. However, the matching bandwidth is extremely narrow, since the passive L, C, and the antenna itself follow the Foster’s reactance theorem [3]. The latter asserts that the reactance must increase as the frequency increases. Figure1a shows an example of adjusting the reactance of a capacitive ESA using an inductor. Both the C and L increase as the frequency increases, following Foster’s reactance theorem. The ESA’s capacitance is completely cancelled by the inductance at a single frequency, implying the matching

Appl. Sci. 2020, 10, 4464; doi:10.3390/app10134464 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 10

Figure 1a shows an example of adjusting the reactance of a capacitive ESA using an inductor. Both the C and L increase as the frequency increases, following Foster’s reactance theorem. The Appl. Sci. 2020, 10, 4464 2 of 9 ESA’s capacitance is completely cancelled by the inductance at a single frequency, implying the matching bandwidth is narrow. To overcome the bandwidth limitation of passive impedance matching,bandwidth a is non-Foster narrow. To circuit overcome (NFC) the matching bandwidth technique limitation employing of passive active impedance components matching, (e.g. a transistor)non-Foster has circuit been (NFC) introduced matching [4,5]. technique The operation employing principle active componentsof an NFC is (e.g., simple, transistor) as depicted has been in Figureintroduced 1b. It [ 4generates,5]. The operation a negative principle C (or L), of which an NFC is against is simple, the asFoster’s depicted reactance in Figure theorem,1b. It generates and thus a broad negative reactance C (or L),cancellation which is againstbandwidth the can Foster’s be ac reactancehieved. Various theorem, non-Foster and thus circuit a broad designs reactance have beencancellation reported bandwidth for the canbroadband be achieved. matching Various of non-Foster small antennas circuit designs[6–11]. haveHowever, been reportedmost of forthem the presentedbroadband only matching the enhancement of small antennas in the [6 antenna’s–11]. However, reflection most coefficient of them presented ( ) after only applying the enhancement the NFC, whichin the antenna’sis not sufficient reflection to coevalidatefficient the (S 11system-w) after applyingide improvement. the NFC, which It is isimportant not suffi cientto examine to validate the signal-to-noisethe system-wide ratio improvement. (SNR) since It the is important active co tomponents examine employed the signal-to-noise in the NFC ratio might (SNR) introduce since the additionalactive components noise into employed the system in the[12,13]. NFC might introduce additional noise into the system [12,13].

(a) (b)

Figure 1. AntennaAntenna reactance reactance cancellation using using ( a)) passive components which follow the Foster’s reactance theorem. ( (b)) Negative Negative reactance generated by the no non-Fostern-Foster circuit matching technique.

In this paper, an NFC design with improved matching bandwidth and and stability stability is is presented. presented. Compared toto the the previously previously designed designed NFC [NFC6], this [6], work this has work a much has smaller a much footprint smaller by shorteningfootprint theby shorteningmicrostrip line,the andmicrostrip thus the line, overall and lossthus and the parasitic overall elossﬀect and originating parasitic from effect the originating NFC can be from reduced. the NFCMore can importantly, be reduced. not onlyMore the importantly, impedance enhancement, not only the butimpedance the received enhancement, power andSNR but enhancementthe received powerafter applying and SNR the enhancement NFC, is presented after andapplying discussed. the NF TheC, NFCis presented was carefully and discussed. designed, focusingThe NFC on was the carefullyreduction designed, of internal focusing loss, resulting on the inreduction an average of internal of 17.3 dBloss, of resulting received in power an average improvement of 17.3 indB the of receivedbandwidth power of 150 improvement to 300 MHz. Toin improvethe bandwidth the stability of 150 of to the 300 NFC, MHz. a two-step To improve validation the stability check strategy of the NFC,of observing a two-step the stability validation condition check instrategy both frequency of observing and time the domainsstability wascondition applied. in Theboth NFC frequency design andis described time domains in detail was in applied. Section2 The. The NFC noise design power is described added by thein detail implemented in Section NFC 2. The was noise measured power addedand the by overall the implemented SNR enhancement NFC was was measured calculated. an Thed the results overall show SNR that enhancement the proposed was NFC calculated. provides Thean average results ofshow 7.3 dB that of enhancementthe proposed ofNFC SNR provides despite ofan the average introduced of 7.3 noise. dB of These enhancement measured of results SNR despiteare discussed of the inintroduced Section3. noise. These measured results are discussed in Section 3.

2. Non-Foster Non-Foster Circuit Circuit Design Design This section first ﬁrst introduces the ESA used in this study. This is important since the NFC design strongly depends on the impedance of the ESA conne connectedcted with it. Next, the proposed NFC design is discussed together with the stability validationvalidation methods and their simulation results.

2.1. Characteristics of Electrically Small Antenna 2.1. Characteristics of Electrically Small Antenna A short monopole was selected as the load. Figure2 shows its measured resistance and reactance A short monopole was selected as the load. Figure 2 shows its measured resistance and together with a picture of the monopole. The length of the monopole is 8.4 cm, corresponding to the reactance together with a picture of the monopole. The length of the monopole is 8.4 cm, quarter-wavelength of 893 MHz. Thus, it can be considered as an ESA at the frequency of interest corresponding to the quarter-wavelength of 893 MHz. Thus, it can be considered as an ESA at the (i.e., 150–300 MHz). The measured resistance and reactance in Figure2a,b, respectively, clearly display impedance characteristics of an ESA: the resistance is low and reactance is high. One can easily notice Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 10

frequency of interest (i.e., 150–300 MHz). The measured resistance and reactance in Figure 2a,b, respectively, clearly display impedance characteristics of an ESA: the resistance is low and reactance is high. One can easily notice that the reactance behavior is similar to Figure 1a: the

Appl.negative Sci. 2020 reactance, 10, 4464 reduces as the frequency increases in a rational manner. This means that as3 of the 9 frequency increases, the negative value of the capacitive reactance decreases (i.e., ). The purpose of the NFC is to generate a negative capacitance complimentary to the antenna’s thatpositive the reactance capacitance, behavior and istherefore, similar tothe Figure input1 a:re theactance negative can reactancebe 0 over reducesa wide asbandwidth. the frequency More increasesspecifically, in a the rational antenna manner. capacitance This means of 8±1 that pF as ca then be frequency cancelled increases, by the NF theC’s negative negative value capacitance of the capacitiveof -8∓1 pF. reactance XC decreases (i.e., XC = 1/jωC). −

(a) (b)

FigureFigure 2. 2. TheThe impedance impedance of of aa short short mo monopolenopole antenna antenna as as a a load: load: (a (a) )resistance resistance and and (b (b) )reactance. reactance.

2.2. TheNon-Foster purpose Circuit of the Design NFC is to generate a negative capacitance complimentary to the antenna’s positive capacitance, and therefore, the input reactance can be 0 over a wide bandwidth. More Figure 3 shows the schematic of the proposed non-Foster circuit to provide negative specifically, the antenna capacitance of 8 1 pF can be cancelled by the NFC’s negative capacitance of capacitance. Two transistors are cross-coupled± to produce a 180-degree inverted phase from the 8 1 pF. −input∓ along the feedback loop [5]. The transistors used were Avago ATF-53189 [14], which are field 2.2.effect Non-Foster transistors Circuit with Design wideband operation bandwidths of 50 MHz–6.5 GHz. With these basic schematics and selected transistors, the other components were optimized to satisfy the stability Figure3 shows the schematic of the proposed non-Foster circuit to provide negative capacitance. condition described in Section 2.3. A high frequency circuit simulator, Keysight Technologies Two transistors are cross-coupled to produce a 180-degree inverted phase from the input along the Advanced Design System (ADS) [15], was used for the optimization. Table 1 lists the optimized values feedback loop [5]. The transistors used were Avago ATF-53189 [14], which are field effect transistors of other components. The reference impedance (Zref) of the NFC was set to 6 pF considering the with wideband operation bandwidths of 50 MHz–6.5 GHz. With these basic schematics and selected monopole’s capacitance. The values of inductors (LG, LD, LS) and resistors (RG, RD, Rs) connected to transistors, the other components were optimized to satisfy the stability condition described in the gate, drain, and source of the transistors should be carefully chosen to ensure the wideband Section 2.3. A high frequency circuit simulator, Keysight Technologies Advanced Design System stability criterion. As the value of the inductor increases, its self-resonant frequency (SRF) decreases, (ADS)adversely [15], affecting was used the for NFC the optimization. stability [16]. TableThe 1resi listsstor the values optimized are also values important of other since components. the wrong Theselection reference can impedancelead to a generation-negative (Zref) of the NFC wasresistance set to 6that pF goes considering against the the stability monopole’s condition capacitance. [17]. To The values of inductors (LG,LD,LS) and resistors (RG,RD,Rs) connected to the gate, drain, and reduce the loop gain of the transistors for stability, RStab and CStab are set as 51 Ω, 1 pF, respectively. source of the transistors should be carefully chosen to ensure the wideband stability criterion. As the The gate voltage (VGG), drain voltage (VDD), and drain current of the designed circuit are 1.8 V, 5.7 V, valueand 4 of mA, the respectively. inductor increases, its self-resonant frequency (SRF) decreases, adversely affecting the NFC stability [16]. The resistor values are also important since the wrong selection can lead to a generation-negative resistance that goes against the stability condition [17]. To reduce the loop gain of the transistors for stability, RStab and CStab are set as 51 Ω, 1 pF, respectively. The gate voltage (VGG), drain voltage (VDD), and drain current of the designed circuit are 1.8 V, 5.7 V, and 4 mA, respectively. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 10

Appl. Sci. 2020Appl., 10 Sci., 4464 2020, 10, x FOR PEER REVIEW 4 of4 of10 9

FigureFigure 3. 3.A A schematic schematic of of the the proposed proposed non-Foster non-Foster circuit. circuit. Figure 3. A schematic of the proposed non-Foster circuit. Table 1. Optimized values of passive components in Figure3. Table 1. Optimized values of passive components in Figure 3. Table 1. Optimized values of passive components in Figure 3. Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value Zref 6 pF RS 600 Ω Zref 6 pF RS 600 Ω Zref 6 pF RS 600 Ω LG 1 uH RStab 51 Ω LG 1 uH RStab 51 Ω LLDG 1 uH1 uH CStab RStab 1 pF 51 Ω LD LLSD 14.7 uH uH1 uH CG CStab CStab 510 pF 11 pF LS RLGS 4.71.1 uH K4.7Ω uH Cin CG C G 100 pF 510510 pF RG RRDG 1.11.1 K K1.1ΩΩ KΩ Cout CinC in 510 pF 100100 pF RD RD 1.1 K1.1Ω KΩ CoutCout 510510 pF Figure4 showsFigure the4 shows simulated the simulated results of results the NFC of the in theNFC frequency in the frequency range fromrange 50 from MHz 50 toMHz 500 to MHz. 500 Figure 4 shows the simulated results of the NFC in the frequency range from 50 MHz to 500 AccordingMHz. to the According Smith chartto the Smith of the chart reﬂection of the reflection coeﬃcient coefficient (S ) in ( Figure) in Figure4a, the 4a, locus the locus winds winds in in a MHz. According to the Smith chart of the reflection coefficient11 ( ) in Figure 4a, the locus winds in counterclockwisea counterclockwise manner as manner the frequency as the frequency increases increases from 50 from MHz 50 toMHz 500 to MHz. 500 MHz. This This contradicts contradicts the a counterclockwise manner as the frequency increases from 50 MHz to 500 MHz. This contradicts Foster’s reactancethe Foster’s theorem, reactance denoting theorem, that denoting the negative that the capacitance negative capacitance has been successfully has been successfully generated. the Foster’sgenerated. reactance Figure theorem,4b plots thedenoting capacitance that versusthe negative the frequencies. capacitance As can has be beenseen, successfullya negative Figure4b plots the capacitance versus the frequencies. As can be seen, a negative capacitance ranging generated.capacitance Figure ranging4b plots from the 11 capacitance pF to 7.5 pF, andversus approximately the frequencies. 8 pF at 300 As MHz, can isbe generated. seen, a negative from 11 pF to 7.5 pF, and approximately 8 pF at 300 MHz, is generated. capacitance ranging from 11 pF to 7.5 pF, and approximately 8 pF at 300 MHz, is generated.

(a) (b)

Figure 4. Simulation results of the non-Foster circuit: (a) Smith chart of the reﬂection coeﬃcient. (b) Negative capacitance versus frequency. Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 10

Appl. Sci.Figure2020 ,4.10 Simulation, 4464 results of the non-Foster circuit: (a) Smith chart of the reflection coefficient. (b) 5 of 9 Negative capacitance versus frequency. 2.3. Non-Foster Circuit Stability Check 2.3. Non-Foster Circuit Stability Check In common stability criteria for a 2-port network such as the Llewellyn-Rollett port test, the In common stability criteria for a 2-port network such as the Llewellyn-Rollett port test, the network is stable if there are no internal poles or zeros in the right-hand plane (RHP) for a complex network is stable if there are no internal poles or zeros in the right-hand plane (RHP) for a complex plane analysis [18]. However, this is not the case for an NFC since the negative impedance often plane analysis [18]. However, this is not the case for an NFC since the negative impedance often provides poles and zeros in the RHP. Instead, the stability of an NFC is often tested by checking the provides poles and zeros in the RHP. Instead, the stability of an NFC is often tested by checking the short-circuit stability (SCS) or open-circuit stability (OCS) conditions. For the NFC connected with an short-circuit stability (SCS) or open-circuit stability (OCS) conditions. For the NFC connected with antenna, the OCS condition is applied [5], and can be written as an antenna, the OCS condition is applied [5], and can be written as

|Z|ZAntAnt| >| |>Z |ZNFCNFC|,|, (1) (1)

Figure 5. A comparison of the magnitudes of the antenna and non-Foster circuit impedance to check Figure 5. A comparison of the magnitudes of the antenna and non-Foster circuit impedance to check the open-circuit stability criterion. the open-circuit stability criterion. However, the OCS criterion assumes the network is dispersionless. In fact, no circuit is dispersionlessHowever, inthe the OCS real criterion world. Thereassumes is unavoidable the network coupling is dispersionless. between transmission In fact, no linescircuit and is parasiticdispersionless components in the that real can world. cause There undesirable is unav smalloidable oscillations coupling and between possibly transmission diverge as the lines currents and travelparasitic through components the NFC’s that feedback can cause loop. undesirable Thus, it is important small oscillations to check the and transient possibly response diverge in the as time the domaincurrents [ 16travel,18] inthrough addition the to theNFC’s OCS feedback criterion inloop. the frequencyThus, it is domain. important By observingto check the transienttransient response,response thein the sign time of the domain time constants [16,18] in (τ addition= RC and toL the/R )OCS can becriterion identiﬁed. in the If the frequency sign of τ domain.is negative, By theobserving circuit isthe unstable transient and response, the transient the sign response of the divergestime constants as illustrated ( in Figure6a.) can However, be identified. if the signIf the of signτ is positive,of is negative, the transient the circuit response is unstable damps down and th ande transient converges response as the time diverges passes as (Figure illustrated6a). Thein Figure transient 6a. response However, of theif proposedthe sign NFCof isis shownpositive, inFigure the transient6b. Depending response onthe damps combinations down and of resistor-inductor-capacitorconverges as the time passes (RLC) (Figure components, 6a). The some transient NFC response designs satisﬁed of the proposed the OCS criterion NFC is butshown failed in toFigure demonstrate 6b. Depending convergence on the forcombinations the transient of response. resistor-inductor-capacitor The optimized RLC (RLC) values components, in Table1 satisfy some bothNFC thedesigns OCS andsatisfied transient the responseOCS criterion requirements. but failed to demonstrate convergence for the transient response. The optimized RLC values in Table 1 satisfy both the OCS and transient response requirements. Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 10 Appl.Appl. Sci. Sci.2020 2020, 10,, 10 4464, x FOR PEER REVIEW 66 of of 9 10

(a) (b) (a) (b) Figure 6. The transient responses of non-Foster circuits: (a) Examples of stable and unstable FigureFigure 6. The6. The transient transient responses responses of non-Foster of non-Foster circuits: circuits: (a) Examples (a) Examples of stable andof unstablestable and transient unstable transient responses. (b) The transient response of the proposed non-Foster circuit. responses.transient ( bresponses.) The transient (b) The response transient of theresponse proposed of the non-Foster proposed circuit. non-Foster circuit. 3. Fabrication and Measurement of Non-Foster Circuit 3. Fabrication3. Fabrication and and Measurement Measurement of of Non-Foster Non-Foster Circuit Circuit Having validated the NFC performance using simulations, the optimized NFC was fabricated HavingHaving validated validated the the NFC NFC performance performance using using simulations, simulations, the optimizedthe optimized NFC NFC was fabricatedwas fabricated as as shown in Figure 7. It was implemented on an FR-4 substrate with a footprint of 14.4 mm × 20 mm, shownas shown in Figure in Figure7. It was 7. It implementedwas implemented on an on FR-4 an FR-4 substrate substrate with with a footprint a footprint of 14.4 of 14.4 mm mm20 × 20 mm, mm, which is smaller than the previous report [6]. It was miniaturized by reducing the× length of whichwhich is smalleris smaller than than the previous the previous report [report6]. It was [6]. miniaturized It was miniaturized by reducing by the reducing length of the microstrip length of microstrip lines connecting the transistors and RLC components. This also reduced the overall losses linesmicrostrip connecting lines the connecting transistors the and transistors RLC components. and RLC Thiscomponents. also reduced This thealso overall reduced losses the overall consumed losses consumed by the NFC, resulting in the use of lower R values to satisfy the stability conditions. byconsumed the NFC, resulting by the NFC, in the resulting use of lower in the R use values of lower to satisfy R values the stabilityto satisfy conditions. the stability conditions.

Figure 7. The fabricated non-Forster circuit prototype. Figure 7. The fabricated non-Forster circuit prototype. 3.1. Measurement of ReflectionFigure Coefficient 7. The fabricated non-Forster circuit prototype. 3.1. Measurement of Reflection Coefficient 3.1.Figure Measurement8a is a picture of Reflection of the Coefficient small monopole and NFC assembly. A network analyzer (Anritsu MCS2038C)Figure was 8a connected is a picture to the of input the small port ofmonopole the NFC toand measure NFC assembly. the S11. The A network measured analyzerS11 is shown (Anritsu Figure 8a is a picture of the small monopole and NFC assembly. A network analyzer (Anritsu in FigureMCS2038C)8b. The comparisonwas connected made to herethe input is with port and of without the NFC the to NFC. measure The latter the means. The the measured monopole is MCS2038C) was connected to the input port of the NFC to measure the . The measured is wasshown directly in connected Figure 8b. to The the comparison network analyzer. made here As observed, is with and the without measured the SNFC.11 without The latter the NFC means is the shown in Figure 8b. The comparison made here is with and without the NFC. The latter means the highermonopole than –2 was dB over directly the wholeconnected frequency to the range,network 50–500 analyzer. MHz. As This observed, is due tothe the measured high capacitance without preventingmonopole the was monopole directly connected from reaching to the the network resonance analyzer. as described As observed, in Section the measured 2.1. Contrarily, without the the NFC is higher than –2 dB over the whole frequency range, 50–500 MHz. This is due to the high S the< NFC10 dB is bandwidthhigher than is– 60–4002 dB over MHz the whenwhole the frequency NFC is connectedrange, 50–500 to the MHz. monopole. This is due This to proves the high 11 capacitance− preventing the monopole from reaching the resonance as described in Section 2.1. thatcapacitance the NFC successfully preventing removes the monopole the positive from capacitance reaching ofthe the resonance monopole as by described generating in a Section sufficient 2.1. Contrarily, the dB bandwidth is 60–400 MHz when the NFC is connected to the amountContrarily, of negative the capacitance.dB bandwidth is 60–400 MHz when the NFC is connected to the monopole. This proves that the NFC successfully removes the positive capacitance of the monopole monopole. This proves that the NFC successfully removes the positive capacitance of the monopole by generating a sufficient amount of negative capacitance. by generating a sufficient amount of negative capacitance. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 10

Appl. Sci. 2020, 10, 4464 7 of 9

(a) (b)

FigureFigure 8. The 8. measurementThe measurement of the reflectionof the reflection coefficient coefficien of the monopolet of theand monopole non-Foster and circuit non-Foster assembly: circuit (a) Aassembly: picture of the(a) fabricatedA picture non-Fosterof the fabricated circuit connected non-Foster to thecircuit monopole. connected (b) The to measuredthe monopole. reflection (b) The coeffimeasuredcient with reflection and without coefficient the non-Foster with and circuit. without the non-Foster circuit.

3.2.3.2. Measurement Measurement of Signal-to-Noise of Signal-to-Noise Ratio Ratio As describedAs described in the in introduction,the introduction, the broadband the broadbandS11 does notdoes guarantee not guarantee the eff ectivenessthe effectiveness of the of NFCthe since NFC the since NFC itselfthe NFC can generate itself can additional generate noise addi thattional may noise adversely that may influence adversely a systematical influence a figure-of-merit,systematical SNR.figure-of-merit, With this issue SNR. in With mind, this we issu proceedede in mind, to we measure proceeded SNR to with measure and without SNR with the and NFC,without following the theNFC, measurement following the setups measurement depicted insetups Figure depicted9. The transmitted in Figure 9. signals, The transmitted originated signals, by a signaloriginated generator, by a were signal captured generator, by awere spectrum captured analyzer by a inspectrum the receiving analyzer end. in The the receivedreceiving power end. The and noise power read by the spectrum analyzer are denoted as (S ,N ) without the NFC and received power and noise power read by the spectrum analyzerESA are denotedESA as (SESA, NESA) without (S ,N ) with the NFC, respectively. With them, the SNR enhancement due to the NFC ESAthe+NFC NFC andESA+ (SNFCESA+NFC, NESA+NFC) with the NFC, respectively. With them, the SNR enhancement due to canthe becalculated NFC can be by calculated by

SNR enhancement = (S + S ) (N + + N ) (2) Appl. Sci. 2020, 10, x FOR PEER REVIEW ESA NFC − ESA − ESA NFC ESA 8 of 10

(2)

SNR enhancement =

Figure 9. The measurement setup for signal-to-noise ratio measurement without and with the non-Foster circuit connected.Figure 9. The measurement setup for signal-to-noise ratio measurement without and with the non-Foster circuit connected.

(SESA+NFC SESA) means Received power enhancement, and (NESA+NFC + NESA) means Figure− 10a shows the received power recorded by the spectrum analyzer with and without the Added noise. NFC. Their difference is labelled as “Improvement”. There are some fluctuations, but the power Figurereceived 10a shows with the the NFC received equipped power shows recorded higher byvalu thees spectrumthan the antenna-only analyzer with case and(i.e. without the the NFC. TheirNFC) di ﬀthroughouterence is labelledthe frequency as “Improvement”. range of 150–300 MHz. There The are average some power ﬂuctuations, improvement but the achieved power by using the NFC is 17.3 dB. Subsequently, Figure 10b shows the noise power added by the NFC. It can be observed that the NFC adds fluctuating noise, which peaks at more than 7 dB for some frequency points. These fluctuations come from the thermal noise increase and decrease as the currents travel in the feedback loop of the NFC. The added noise base is around 7 dB, and for the noise-peaking frequencies, it is around 14 dB. Finally, the SNR enhancement by the NFC was calculated by subtracting the received power enhancement from the added noise power. As depicted in Figure 11, the SNR enhancement values also significantly fluctuate due to the noise fluctuation, implying that the NFC is not effective in improving the reception of the communication system for certain frequencies. The fluctuation does not exceed the stability limit but can adversely affect the SNR of the system. Figure 11 also shows a smoothed curve of SNR enhancement. It indicates that an average of 7.2 dB of SNR enhancement can be achieved if the noise fluctuation can be controlled by implementing a cooling or damping device on the NFC.

(a) (b)

Figure 10. The power measurement data with and without the non-Foster circuit: (a) received power and (b) noise power. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 10

Figure 9. The measurement setup for signal-to-noise ratio measurement without and with the non-Foster circuit connected.

Appl. Sci. 2020Figure, 10, 4464 10a shows the received power recorded by the spectrum analyzer with and without8 of 9 the NFC. Their difference is labelled as “Improvement”. There are some fluctuations, but the power received with the NFC equipped shows higher values than the antenna-only case (i.e. without the receivedNFC) with throughout the NFC the equipped frequency shows range higher of 150–300 values MHz. than theThe antenna-only average power case improvement (i.e. without achieved the NFC)by throughout using the NFC the frequency is 17.3 dB. range Subsequently, of 150–300 Figure MHz. The10b averageshows the power noise improvement power added achieved by the NFC. by It usingcan the be NFC observed is 17.3 dB.that Subsequently, the NFC adds Figure fluctuating 10b shows noise, the noisewhich power peaks added at more by the than NFC. 7 dB It can for be some observedfrequency that the points. NFC addsThese fluctuating fluctuations noise, come which from peaks the at thermal more than noise 7 dB increase for some frequencyand decrease points. as the Thesecurrents fluctuations travel comein the from feedback the thermal loop of noisethe NFC. increase The andadded decrease noise base as the is currentsaround 7 travel dB, and in thefor the feedbacknoise-peaking loop of the frequencies, NFC. The added it is noisearound base 14 is dB. around Finally, 7 dB, the and SNR for the enhancement noise-peaking by frequencies, the NFC was it is aroundcalculated 14 dB. by Finally, subtracting the SNR the enhancement received power by the enhancement NFC was calculated from bythe subtracting added noise the received power. As powerdepicted enhancement in Figure from 11, the the added SNR enhancement noise power. Asvalues depicted also insignificantly Figure 11, thefluctuate SNR enhancementdue to the noise valuesfluctuation, also significantly implying fluctuate that the due NFC to is the not noise effective fluctuation, in improving implying the that reception the NFC of is the not communication effective in improvingsystem thefor receptioncertain frequencies. of the communication The fluctuation system does for not certain exceed frequencies. the stability The limit fluctuation but can adversely does not exceedaffect the the SNR stability of the limit system. but can Figure adversely 11 also affect shows the SNR a smoothed of the system. curve Figure of SNR 11 alsoenhancement. shows a It smoothedindicates curve that of an SNR average enhancement. of 7.2 dB Itof indicates SNR enhancement that an average can be of achieved 7.2 dB of if SNR the enhancementnoise fluctuation can can be achievedbe controlled if the noiseby implementing fluctuation can a cooling be controlled or damping by implementing device on the a coolingNFC. or damping device on the NFC.

(a) (b)

Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 10 FigureFigure 10. The 10. powerThe power measurement measurement data data with with and withoutand without the non-Foster the non-Foster circuit: circuit: (a) received (a) received power power and (andb) noise (b) noise power. power.

Figure 11. Signal-to-Noise Ratio enhancement due to the non-Foster circuit. 4. Conclusions Figure 11. Signal-to-Noise Ratio enhancement due to the non-Foster circuit.

A4. non-Foster Conclusion circuit was designed to improve the SNR of an electrically small monopole antenna. The cross-coupled structure of the NFC was optimized using a high frequency circuit simulation A non-Foster circuit was designed to improve the SNR of an electrically small monopole software, Keysight ADS, and component values and bias voltages were carefully chosen to meet antenna. The cross-coupled structure of the NFC was optimized using a high frequency circuit stability criteria. A two-step stability check was used: 1) An open-circuit stable condition in the simulation software, Keysight ADS, and component values and bias voltages were carefully chosen frequency domain and 2) The convergence of transient responses in the time domain. The measured to meet stability criteria. A two-step stability check was used: 1) An open-circuit stable condition in the frequency domain and 2) The convergence of transient responses in the time domain. The measured S11 < –10 dB bandwidth after applying the NFC was 60–400 MHz, broad enough to cover several VHF and UHF communication bands with an antenna length less than 10 cm. The received power measurement also showed promising results that are more than 17 dB of improvement after applying the NFC. However, the NFC accompanies a highly fluctuating noise power of 7 to 14 dB that adversely affects the SNR. Author Contributions: Conceptualization, J.-Y.C.; Data curation, Y.-H.L and S.-y.C.; Formal analysis, Y.-H.L.; Funding acquisition, J.-Y.C.; Methodology, Y.-H.L.; Resources, S.-y.C.; Supervision, J.-Y.C.; Validation, S.-y.C.; Visualization, Y.-H.L.; Writing – original draft, Y.-H.L.; Writing – review & editing, J.-Y.C.

Funding: This work has been supported by the Future Combat System Network Technology Research Center program of Defense Acquisition Program Administration and Agency for Defense Development. (UD190033ED)

Conflicts of Interest: The authors declare no conflicts of interest.

References

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S11 < –10 dB bandwidth after applying the NFC was 60–400 MHz, broad enough to cover several VHF and UHF communication bands with an antenna length less than 10 cm. The received power measurement also showed promising results that are more than 17 dB of improvement after applying the NFC. However, the NFC accompanies a highly ﬂuctuating noise power of 7 to 14 dB that adversely aﬀects the SNR.

Author Contributions: Conceptualization, J.-Y.C.; Data curation, Y.-H.L. and S.-y.C.; Formal analysis, Y.-H.L.; Funding acquisition, J.-Y.C.; Methodology, Y.-H.L.; Resources, S.-y.C.; Supervision, J.-Y.C.; Validation, S.-y.C.; Visualization, Y.-H.L.; Writing—original draft, Y.-H.L.; Writing—review & editing, J.-Y.C. All authors have read and agreed to the published version of the manuscript. Funding: This work has been supported by the Future Combat System Network Technology Research Center program of Defense Acquisition Program Administration and Agency for Defense Development (UD190033ED). Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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