Non-Foster Matching Circuit Design via Tunable Inductor

Research ArticleNon-Foster Matching Circuit Design via Tunable Inductor forVLF Receive Loop Antennas

Yalong Yan Chao Liu HuaningWu and Yinghui Dong

Department of Electronic Engineering Naval University of Engineering Wuhan 430033 China

Correspondence should be addressed to Chao Liu liuchao0817sinacom

Received 15 March 2017 Revised 28 August 2017 Accepted 1 October 2017 Published 24 October 2017

Academic Editor Toni Bjorninen

Copyright copy 2017 Yalong Yan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a non-Foster matching circuit (NFC) for very low frequency (VLF) receive loop antennas A 1 lowast 1mVLF receiveloop antenna was designed with a CMOS switch-based tunable inductor built into the NFC The NFC can be applied to differentVLF loop antennas by adjusting the number and inductance of the cells in the tunable inductor A loop antenna was matched tothe designed NFC with minus10 dB 11987811 fractional bandwidth marking a 383 improvement as well as enhanced transducer gain (11987821)compared to most bands in passive matching (over 15ndash30 kHz)The noise and received signal-to-noise ratio (SNR) of the matchingnetwork were assessed to find that with a low noise floor level (4 dB) receiver the SNR of the passive loaded antenna performsbetter than the non-Foster loaded antenna in VLF

1 Introduction

Electrically small antennas (ESAs) are a popular researchsubject because they are the enabling technology for wirelesscommunication applications ESAs infamously suffer fromhigh radiation quality factor (119876) value and a correspondingefficiency-bandwidth tradeoff when using passive impedancematching Wheeler and Chu [1 2] provided very usefuldescriptions of this fundamental tradeoff limit The limitcan be overcome by adding active elements to the antennarsquosmatching circuit and ldquonon-Fosterrdquo elements are particularlyeffective due to their ldquonegative capacitancerdquo or ldquonegativeinductancerdquo characteristics These negative elements existonly theoretically an equivalent circuit for example negativeimpedance converter (NIC) or negative impedance inverter(NII or NIV) is necessary to invert the passive capacitor to anegative capacitor or inductor

Several NFC topologies have been reported to date [3ndash5]most ofwhichwere designed for enhanced stability and band-width performance Earlier researchers mainly concentratedstudies on the high frequency (HF) band [6ndash10] DifferentNFCs including CMOS based NFC [11] diode based NFC[12] and amplifier based NFC [13] have been matched to var-ious types of antennas including the monopole antenna [14]

loop antenna [15] Egyptian axe dipole antenna [16]microstrip leaky-wave antenna [17] and parasitic array [18]with mostly favorable results Also negative non-Fosterimpedances are not absolutely stable circuits which couldbe a serious problem in practical application the stabilityof negative impedances in several circuits was analyzedincluding series C-C tank circuit parallel C-C tank circuitand series- parallel C-C tank circuit [14 19]

There are three main obstacles to the practical realizationof NFCs First little is known about the antennasrsquo operationfrequency band enlargement process especially below HFVLF receive loop antennas which are common in submarinesas a signal reception component are a good example of thisSubmarines under water usually receive VLF signal which istransmitted by large VLF transmitting stations although theVLF signal could go through the water the signal bandwidthand rate received by the submarine are relatively low Nowthe receive antennas equipped on the submarine are passiveantennas such as trailing wire antennas (about 200m long)or loop antennas The bandwidth of the signal is limited byusing this type of antennas so improving the bandwidth andSNR of the received signal is very necessary To the best ofthe authorsrsquo knowledge the only NFC design in VLF wasdescribed by Albee [20] from 14 to 38 kHz where a variable

HindawiInternational Journal of Antennas and PropagationVolume 2017 Article ID 6198686 10 pageshttpsdoiorg10115520176198686

2 International Journal of Antennas and Propagation

Litz coil(10 circles)

1m

1m

25 cm

(a) (b)

Figure 1 (a) Schematic diagram of rectangle loop antenna with shield case (b) Photograph of rectangle loop antenna with shield case (validat a single frequency)

capacitance was matched passively to the antenna and theantennarsquos reactance was canceled by a negative reactancegenerated by a single NFC This matching circuit can onlyfunction at a single frequency or in a small bandwidth asopposed to the whole bandwidth The second obstacle isthe lack of a negative tunable inductor suitable for VLFreceive antenna matching Previous researchers have pre-sented methods in ultrahigh frequency (UHF) [21 22] anddid not address the matching process between the antennasand the tunable NFCsThe third obstacle is the general lack ofresearch on NFC noise and SNR performance Sussman-Fortand Rudish [5] and Jacob and Sievenpiper [23] provided con-flicting results on SNR performance in HFThe present studywas to run a noise and gain test on the receiving system toexamine the NFC networkrsquos SNR performance in VLF

The results presented below suggest that it is feasible tomodify a voltage controlled tunable inductor integrated inNFC for VLF receive antennas Different VLF receive loopantennas can be applied to the designed NFC by switchingeach CMOS ldquoonrdquo or ldquooffrdquo as necessary The noise and gain ofthe passive and non-Foster matching network were alsomeasured to test the actual SNR performance of the VLFreceiving systemAll the datawas analyzed in the small-signalregime (eg receive antennas)

The remainder of this paper is organized as follows Sec-tion 2 presents the design and model method of the receiveloop antenna The design topology of the tunable inductorwhich is integrated in theNFC is presented in Section 31 Sec-tion 32 describes the application of the inductor tunableNFCto the receive antenna in VLF Section 4 presents the gainnoise and SNR of the non-Foster network Section 5 providesa brief conclusion

2 Antenna Design and Model

21 Antenna Design The influence of a noise source near anantenna can be minimized by selecting the proper electric or

magnetic receive antenna and the SNR of the antenna canalso be improved For instance the response of a loop antennawhich has a shield case is 30 dB lower than a same effectiveheight whip antenna under a 0005120582 distance from the staticnoise source (100m at the frequency of 15 kHz) [24]

A 1lowast 1m rectangle loop antennawith a polyvinyl chloride(PVC) pipe shield case was selected as the VLF receiveantenna in this study the loop antenna was designed by litzwire the litz wirewas circled inside a shield pipe and the PVCpipe acts as a supporting function of the litzwireMany circlesof litz wire (99 circles per string 20 strings and 1980 circlesin total) could increase the antennarsquos efficient height Alsoaccording to [24] the signal reception antennas which sub-mains usually use are trailing wire antennas or loop antennasas the trailingwire (around 200m) is too long for experimentso when selecting the type of VLF receive antenna the loopantenna became the first choice As the antenna is woundwith litz wire inside the pipe it is difficult to model it inelectromagnetism (EM) simulation software such as FEKOor HFSS The impedance characteristics of the designedloop antenna were measured and simulated both in practiceand in FEKO the simulation was nearly 120 h long and theVLF results differed substantially

We designed a practical VLF receive loop antenna asthe measurement target Its input impedance characteristicswhich served as parameters for the subsequent design wereobtained by vector network analyzer (VNA) from 15 to30 kHz A schematic diagram of the rectangle loop antenna isshown in Figure 1(a) Figure 1(b) shows a photograph of theantennaThe loop antennarsquos inductancewas determined by (1)as the Litz coil was being wound [24]

119871119886 = 12058311988611989921199012 (1)

International Journal of Antennas and Propagation 3

S(2 1)

S(1 1)

minus14

minus12

minus10

minus8

S(2

1)(d

B)

minus06

minus04

minus02

0S(1

1)(d

B)

15 2520 30Frequency (kHz)

(a)

Antenna equivalent inductanceCurve fitting

06496

06498

065

06502

06504

06506

Indu

ctan

ce (m

H)


(b)

Figure 2 Loop receive antenna measurement data (a) 119878-parameters of the VLF loop receive antenna (b) equivalent inductance of the VLFreceive loop antenna

Port 1 Port 2

(a) (b)

RlZ0

jXaZ0

jXa

Rr

Rl

Z0

N 1

Figure 3 The equivalent circuit of an electrically small antenna (b) two-port representation of an antenna (radiation resistance replacedwith a transformer of free space) (valid at a single frequency)

where 119886 is the average radius of the coil 119899 is the turns of thecoil and120583 is the permeability of the coilrsquosmaterial119901 is relatedto the form factor119898119891 of the loop antenna

119898119891 = 1199042119886 (2)

where 119904 is the cross-sectional area of the loop antenna When119898119891 lt 02119901 = (1 + 11989811989126 ) ln( 81198981198912) + 0411198981198912 minus 170 (3)

We next obtained the 119878-parameters of the loop antennawith a VNA as shown in Figure 2(a) Figure 2(b) shows theantennarsquos equivalent inductance

22 Antenna Model A two-port antenna model to matchthe simulated NFC targets was used in the Advanced DesignSystem (ADS) simulation software The equivalent circuit(valid at specific frequency) of the antenna is shown inFigure 3(a) where [25]

119885119886 = 119877119886 + 119895119883119886 = 119877119903 + 119877119897 + 119895119883119886119877119903 = 119890119903119877119886119877119897 = (1 minus 119890119903) 119877119886

(4)

119885119886 denotes the complex input impedance of the antenna 119877119903represents the radiation resistance 119890119903 denotes the radiationefficiency119877119897 represents the dissipative loss resistance and119883119886is the antennarsquos reactance


SW1 SW2 SW3 SW4

L1 L2 L3 L4

L5 L6 L7 L8

(a)

SimMeas

SW1 on SW1ndashSW4 off

SW2 on SW1 SW3 SW4 off




minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

Real

ized

indu

ctan

ce (m

H)

(b)

Figure 4 (a) Series-connected tunable inductor fabricated in the NFC (b) the simulated and measured inductance of the tunable inductor

The radiation resistance represents power that is ldquodeliv-eredrdquo by the antenna to the external environment (377Ω) wereplaced the radiation resistance with a transformer to theimpedance of free space or more conveniently to any portimpedance that we wish (such as 50Ω) Figure 3(a) can betransformed to Figure 3(b) as a result where the turns-ratioof the transformer is given by

119873 = radic 1198771199031198850 (5)

As the reactance of the loop antenna in VLF has inductiveproperties the equivalent inductance can be derived asfollows

119871 = 119883119886(2 lowast 120587 lowast 119891) (6)

where1198850 is the desired port impedance We set1198850 to 50Ω inorder to match the designed loop antennaThe turns-ratio ofthe transformer and the equivalent inductance of the antennacan be calculated at each frequency according to (5) and (6)The 119878-parameters of the loop antenna obtained can beimported to the two-port network in a specific format (suchas dataset or touchstone) in the circuit simulator accordinglyWhen port 2 of the two-port network is terminated in thesystem impedance (1198850) the antennarsquos input impedance canbe obtained as follows [4]

119885119886 = 1198850 1 + 119878111 minus 11987811 (7)

3 NFC Design

31 Tunable Inductor A ldquotunable-negative-inductiverdquoNFC isnecessary to match VLF loop antennas with different equiv-alent inductance so a tunable inductance cell should be

designed and fabricated in the NFC Capacitive frequencytuning in integrated circuits is easily implemented by usingvaractors or switched-capacitor arrays but inductive tuningis rarely used because there is no inherently tunable devicethe quality factor is usually insufficient compared to capaci-tors

A voltage controlled tunable inductor which consists ofchip winding inductors and MOSFET switches is proposedhere as shown in Figure 4(a) The inductor array is series-connected and CMOS switches determine the number ofunit inductors 1198711ndash1198717 were set to 01mH and 1198718 was set to008mH in order to match the designed antennaWhen SW4on SW1ndashSW3 off and 1198711ndash1198718 function in the circuit theinductance of the array was 078mH When SW3 on SW1SW2 and SW4 off and 1198711ndash1198713 and 1198715ndash1198717 function in thecircuit the inductance of the array was 06mH When SW2on SW1 SW3 and SW4 off and 1198711-1198712 and 1198715-1198716 functionin the circuit the inductance of the array was 04mH WhenSW1 on SW2ndashSW4 off and 1198711 and 1198715 function in the circuitthe inductance of the array was 02mH Compared to othermethods for securing tunable inductors such as path-short ofspiral inductors [26] and polarity switching of a transformer[27] this approach is programmed and area-efficient Unlikethe previously proposed tunable inductor at nH level [22 23]this inductor can be tuned to mH level which is suitable fornon-Foster matching in VLF

After the inductor array fabricated in the NFC which isshown as in Figure 5(a) the negative inductance of this NFCwas simulated inADS andmeasured by LCRmeterTherewasa significant disparity between the simulated and measureddata (Figure 4(b)) especially at small mH levels because theexcitation voltage was only set to 3V in the simulation toensure that the transistors in the NFC functioned properlythe excitation voltage is limited to 2V in the LCR meterThe difference in excitation voltage caused the split betweensimulation and measurement inductance data


M4

M1

L2M2

L7

Q1

L1

Q2

L8L4

L5

M3L3

L6

Port1 Port2

L0

L9 = 01 mH

V_DC = 31 V

R4 = 80 kOhmR5 = 80 kOhm

C3 = 1 uF C4 = 1 uF

R3 = 10 kOhmR1 = 100 Ohm

R6 = 500 Ohm

C1 = 01 uF

C2 = 01 uF

R2 = 100 Ohm

+

++

++

minus

minusminus

minusminus

s

s

s

s

(a)

Port 1 Port 2

Inductorcells

Switches

(b)

Figure 5 (a) Floating two-port ldquotunable-negative-inductiverdquo NFC for VLF receive antenna (b) Photograph of the NFC applied in VLF(45mm length 35mm width)

32 NFC Realization A floating open-circuit stable config-uration of Linvillrsquos NFC which is shown in Figure 5(a) wasimplemented with a low-noise NPN silicon bipolar transistor(NEC NE85630) on a standard 15mm thick PCB board(Figure 5(b)) where 1198711ndash1198718 and the four NMOS switchesconstitute the loaded tunable inductor to match differentantennas The transistors were modeled based on their 119878-parameters so the performance of the NFC designed accord-ing to calculated element values was not ideal After port 2 ofthe designed NFC connected to the antenna model we firstcalculated the values of 1198774 1198775 [28] and for better matchingperformance the values of 1198771 1198772 1198774 1198775 11987110 and supplypower119881 DC were optimized by genetic algorithm in ADS toaccount for this Two objective functions were set in the ADSto optimize control unit The first one is

minus20 lt abs (imag (119885in1)) lt 20 (8)

The second one is

minus20 lt abs (real (119885in1) minus 50) lt 20 (9)

With the introduction of the two objective functionsabove the elementsrsquo values were reconfigured the inputresistance of the matching circuit can be closer to 50Ω andthe input reactance can be closer to 0Ω

During the simulation we found that 1198719 and the load1198710 were the two most sensitive components in the NFC 1198719relates more closely to 11987811 of the two-port matching networkwhich changes 11987811 minimum valuersquos corresponding fre-quency point 1198710 determines the magnitude of the minimum

Port 1 Port 2

+

minus

+

minus

I1 I2

ZＣＨ1 = minusKZL2

(K gt 0)ZL1 V1


(K gt 0)ZL2V2NFC

Figure 6 Ideal NFC diagram

11987811 value and maximum 11987821 value To this effect the values of1198719 and 1198710 should be slightly tuned to ensure favorable NFCperformance after optimization in addition to the selection ofcomponents inHF1198773 is mainly used in the control of currentmutation situations

33 Stability Analysis The stability of the NFC is also animportant concern The ideal NFC diagram is shown inFigure 6 One port of an NIC must be an OCS (open-circuitstable) port with the other port then being SCS (short-circuitstable) [5] in Figure 6 Then with port 1 the OCS port opencircuited and with any passive impedance terminating port2 the resulting network will be stable Of more interest isa corollary to the previous theorem which may be statedas follows The inherent conditional stability of an NICconstrains the magnitude of the impedances that can beconnected to the OCS port and to the SCS port [5]


Source stable factorLoad stable factor

282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor

Figure 7 Stable factor of source and load port of the non-Fostermatching network

This means that at the OCS port 1 at the very least thefollowing is required 100381610038161003816100381611988511987111003816100381610038161003816 gt 1003816100381610038161003816119885in1

1003816100381610038161003816 (10)

Similarly at the SCS port 2 we want100381610038161003816100381611988511987121003816100381610038161003816 lt 1003816100381610038161003816119885in21003816100381610038161003816 (11)

This indicates that to maintain the stability of the circuitThe absolute ndash119871 (inductance) value produced by the NFCshould be greater than the loadrsquos (loop antenna) equivalentinductance value in an OCS condition In our study theabsolute value of theNFC is about 078mH (Figure 4(b) SW4on SW1ndashSW3 off condition) and the loop antennarsquos equiva-lent inductance is about 065mH (Figure 2(b)) which meetsthe circuit stability requirement

After the NFC designed the circuit stability was verifiedvia transient simulation in ADS which is one of the bestapproaches to verify stability among the numerical methodsbased on our experience with NFC circuit measurementTheload and sourcersquos stability can be analyzed in the two-port net-workThe stability factor of the NFCrsquos load and source can beexpressed as

120583 = (1 minus 10038161003816100381610038161198781110038161003816100381610038162)(100381610038161003816100381611987822 minus Δ11987811lowast1003816100381610038161003816 + 100381610038161003816100381611987812119878211003816100381610038161003816)1205831015840 = (1 minus 10038161003816100381610038161198782210038161003816100381610038162)(100381610038161003816100381611987811 minus Δ11987822lowast1003816100381610038161003816 + 100381610038161003816100381611987812119878211003816100381610038161003816)

(12)

Here 120583 (1205831015840) stands for the distance from the center ofthe smith chart to the nearest unstable-input load (source)stability circle If 120583 gt 1 (1205831015840 gt 1) the nearest loadrsquos (sourcersquos)impedance value is outside the unity reflection coefficientrim of the Smith chart and cannot represent a passiveimpedance which means therersquos no unstable passive load(source) impedance in this matching network

The designed NFCrsquos stable factors of source and load areshown in Figure 7The values of 120583 and 1205831015840 are greater than onewhich means the network is in a stable condition

4 Test and Results

The proposed circuit was tested by matching the loopantenna described in Section 2 with equivalent inductanceof 065mH According to the simulation we ran to optimizeNFC performanceThe negative inductance generated by theNFC can be tuned by changing the inductor cellsrsquo values andthe switch numbers which would allow different antennasto be applied to the NFC in practice A ldquobest-effortrdquo passivematching network with a resonance frequency of 225 kHzwas designed for comparison with the non-Foster matchingnetwork The passive matching network is formed by an Lnetwork which contains two capacitances as shown in Fig-ure 8The values of the capacitances can be obtained not onlyby existing formulas but also by the control unit Smith ChartMatching in ADS The latter method is more convenient andprecise after comparison One can obtain the following valuesof the capacitances when designing a perfect matching at225 kHz 1198621 = 514 nF 1198622 = 844 nF41 119878-Parameter Measurements The two-port 119878-parametersof the matching network were simulated and measured atminus30 dBm source power withM1ndashM3 in the ldquooffrdquo case andM4in the ldquoonrdquo case by VNA The simulation scheme is roughlysimilar to Figure 8 the L network which contains 1198621 and 1198622was replaced by the NFC designed

When conducting 11987811 measurement the antenna wasconnected to port 2 of the NFC through a 50Ω microstripline and port 1 of theNFCwas connected to port 1 of theVNA(RampS ZVL) The test setup is shown in Figure 9(a) Whenconducting 11987821 measurement as the result is not precise tomeasure 11987821 in the VLF near field by using the receive andtransmit antenna measuring system (referred in reference[23]) we used 119871119886 and 119877119886 to represent the equivalent modelof the antenna and let the signal transfer in electronic com-ponent 119871119886 represents the equivalent inductance of the loopantenna and 119877119886 represents the resistance of the antenna Thevalues of 119871119886 (average 065mH) and 119877119886 (average 35Ω) ateach frequency are obtained by the measured data of theloop antenna in Section 21 The test diagram is shown inFigure 9(b) The test setup is shown in Figure 10

The results can be observed from Figure 11(a) that theminus10 dB 11987811 fractional bandwidth of the NFC loaded case is18 from 15 kHz to 30 kHz marking a 383 improve overthe passive loaded antenna (47) In ideal situation if theNFC is replaced by an ideal negative inductor in series withthe loop antenna the bandwidth would be much larger butFigure 11(a) does not show the same behavior we indicate thatafter the transistors the supply power and other electronicdevices joined in the noise the transistorsrsquo nonideal biasand the circuitrsquos loss all may lead to this ldquonot much largerrdquobandwidth performance comparedwith the passivematchingcase11987821 of the NFC-enhanced antenna was also compared tothat of the passive loaded antenna as shown in Figure 11(b)Although the signal gain provided by the NFC matchingnetwork decreased by 25 maximum at the resonant pointit increased over 15ndash218 kHz and 231ndash30 kHz Thereforethe NFC-enhanced signal gain is superior to that of the


VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus

Expr = ldquoabs(real(Zin1) minus 50)rdquoExpr = ldquoabs(imag(Zin1))rdquo

Z = 50Ohm Z = 50OhmC = 844 nFF = 225 kHz

C2

C2 = 90 o

C = 514 nFF = 225 kHz

C1 File=ldquo15ndash30s2prdquo

C1 = 500 o

Figure 8The designed passive matching circuit for comparison with the non-Foster matching circuit the s2p file is the loop antenna modelGenetic algorithm in ADS was used to optimize the values of 1198621 and 1198622

VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA

PassiveNFCmatching Antenna model

1

2

La

Ra

(b)

Figure 9 (a) 11987811 measurement diagram for non-Foster matched antenna and passive antenna (b) 11987821 measurement diagram for non-Fostermatched antenna and passive antenna (the passive matching and non-Foster matching circuit are attached to the antenna resp)

VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)

Figure 10 (a) 11987811 of NFC matching experiment setup (b) 11987821 of NFC matching experiment setup

passive loaded case over most frequency bands in VLF(15 kHzndash30 kHz)

42 SNR Measurements Non-Foster matching networks caneliminate the gain-bandwidth limitations of passive smallantennas but at the cost of increased noise generated by the

activematching circuit To assess the SNR of the antennawiththe matching circuit we used basically the same proceduresuggested by Sussman-Fort and Rudish [5] the differencebetween our method and Sussmanrsquos is that the measurementsdistance of the TxRx is not the same as we should conductthe SNRmeasurement in far filed of the signal so in the SNR


minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5


Passive SimPassive Meas

Non-Foster SimNon-Foster Meas

(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)

Figure 11 (a) Comparison of measured and simulated 11987811 of NFC and passive matching network under condition of SW1ndashSW3 off and SW4on (b) Comparison of measured and simulated 11987821 of the NFC and passive matching network under condition of SW1ndashSW3 off and SW4 on

TransmitterSpectrumanalyzer

Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB

Measure signal level S0at receiver using antennawith non-Foster matching

Measure signal level S1at receiver using antennawith passive matching

Gain improvement (dB) = (S1 minus S0)

Figure 12 Received SNR of a non-Foster matched antenna compared to that of a passive antenna attached to an amplifier

test in VLF the Tx and Rx system test distance should bemuch further compared to the test in HFThe received signalis transmitted from a VLF transmitting station

The noise signal at the antenna input terminal withand without the matching network was measured with aspectrum analyzer (Agilent N9310A) while the transmitsignal disappearedWhen performing noisemeasurements itis very important to be aware of the sensitivity of the receivernamely its noise floor (NF) Depending on the noise floorthe noise at the terminals of the antenna with and withouta matching circuit may not be detected by the spectrumanalyzer so a low noise preamplifier was attached to the spec-trum analyzer to obtain a receiver that had a low NF (4 dB)under matched conditions

For gain measurement the passive and non-Fostermatching circuits were attached to the spectrum analyzer and

subjected to a test outdoors To access the NFCrsquos far fieldperformance when the received VLF signal was transmittedthrough a VLF transmitting station at fixed time the signaldata was recorded for SNR calculation The measurementsetup is shown in Figure 12

We found that the NFC provided a gain improvementgreater than 0 dB (average 11 dB) over the whole bandwidth(Figure 13(a)) which suggested that the NFC can enhancethe received signal power compared to the passive circuitThe received SNR was calculated according to the differ-ence in gain and noise levels (Figure 13(b)) There was noimprovement in the received SNR over 15ndash30 kHz (averageminus26 dB) which is contradictory to the conclusion providedby Sussman-Fort and Rudish [5] but conforms to Jacob etalrsquos [18] conclusion We found that the NF of the spectrumanalyzer used in these two studies was different ndash the former



Passive gainNFC gain NFC noise

Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)

Gain improvementSNR improvement


minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)

Figure 13 Measurement setup to record (a) gain noise of passive and non-Foster matching network and (b) gain SNR improvement ofpassive and non-Foster matching network

spectrum analyzer has a NF of 8 dB and the latter has a NF of4 dB

In order to analyze this SNR decrease phenomenon wenoted that the noise received by the spectrum analyzer can bedivided into three parts the generated noise in the NFC thereceiverrsquos noise and the environmental noise The receiverrsquosnoise and the environmental noise are the same between thepassive matching case and the NFCmatching case From ourresults where the realized gainrsquos improvement is less than thenoise improvement we can prove that with a higher noisefigure (8 dB) amplifier theNFCnoise signal is decreased to anextremely low value that would get masked by the receiverrsquosnoise floor In our test we took a 4 dB amplifier connected tothe spectrum analyzer in this case the NFC noise signal stillexits and is higher than the receiverrsquos noise floor so the NFCnoise dominates As a result we got a higher noise figure anda lower SNR compared to the passive matching caseWe usedthe NF analyzer as Jacob and Sievenpiper [23] and reacheda similar conclusion Thus the non-Foster loaded antennadoes not provide SNR improvement over the passive loadedantenna using a low noise figure receiver in VLF

5 Conclusion

In this study a 1 lowast 1m loop antenna was matched by aldquotunable-negative-inductiverdquo circuit A modification to thebalancedNFC allowed the circuit tomatch different antennasin VLF The minus10 dB 11987811 fractional bandwidth of the NFCloaded antenna was improved by 383 and the signal gainwas improved over most bands compared to the passiveloaded antenna The realized gain was also improved by anaverage of 11 dB over 15ndash30 kHz Gain and noise measure-ment results further indicated that the NFC loaded antennaexhibited no SNR advantage over the passive loaded antennawith an amplifier As non-Foster receiving systems provide anSNR advantage over passive systems only in cases where thesystem is device-noise limited or when the receiver noise isdominant the noise generated by the NFC would be maskedby the receiverrsquos noise floor and does not affect the overall

system noise figure Therefore our results indicate that thenon-Foster matching circuit can provide a larger bandwidthand gain in low noise receive systems but may not provideany actual SNR performance advantage over passive matchedantennas in VLF

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

References

[1] H A Wheeler ldquoFundamentals limitations of small antennasrdquoProceedings of the IRE vol 35 no 12 pp 1479ndash1484 1947

[2] L J Chu ldquoPhysical limitations of omni-directional antennasrdquoJournal of Applied Physics vol 19 no 12 pp 1163ndash1175 1948

[3] C RWhite J S Colburn and R G Nagele ldquoA non-foster VHFmonopole antennardquo IEEE Antennas and Wireless PropagationLetters vol 11 pp 584ndash587 2012

[4] J T Aberle ldquoTwo-port representation of an antenna with appli-cation to non-foster matching networksrdquo IEEE Transactions onAntennas and Propagation vol 56 no 5 pp 1218ndash1222 2008

[5] S E Sussman-Fort and R M Rudish ldquoNon-foster impedancematching of electrically-small antennasrdquo IEEE Transactions onAntennas and Propagation vol 57 no 8 pp 2230ndash2241 2009

[6] R W Ziolkowski M-C Tang and N Zhu ldquoAn efficientbroad bandwidth high directivity electrically small antennardquoMicrowave and Optical Technology Letters vol 55 no 6 pp1430ndash1434 2013

[7] K A Obeidat B D Raines and R G Rojas ldquoApplication ofcharacteristic modes and non-foster multiport loading to thedesign of broadband antennasrdquo IEEE Transactions on Antennasand Propagation vol 58 no 1 pp 203ndash207 2010

[8] TDebogovic SHrabar and J Perruisseau-Carrier ldquoBroadbandFabry-Perot radiation based on non-Foster cavity boundaryrdquoIEEE Electronics Letters vol 49 no 4 pp 271-272 2013

[9] M Barbuto A Monti F Bilotti and A Toscano ldquoDesignof a non-foster actively loaded SRR and application in


metamaterial-inspired componentsrdquo IEEE Transactions onAntennas and Propagation vol 61 no 3 pp 1219ndash1227 2013

[10] F Albarracın-Vargas E Ugarte-Munoz V Gonzalez-Posadasand D Segovia-Vargas ldquoSensitivity analysis for active matchedantennas with non-foster elementsrdquo Institute of Electrical andElectronics Engineers Transactions on Antennas and Propaga-tion vol 62 no 12 pp 6040ndash6048 2014

[11] A Niang A de Lustrac and S N Burokur ldquoSuperluminalwave propagation in a non-Foster negative capacitor loadedtransmission linerdquo Electronics Letters vol 53 no 8 pp 547ndash5492017

[12] D S Nagarkoti Y Hao D P Steenson L Li E H Linfield andK Z Rajab ldquoDesign of broadband non-foster circuits basedon resonant tunneling diodesrdquo IEEE Antennas and WirelessPropagation Letters vol 15 pp 1398ndash1401 2016

[13] H Yang I Kim and K Kim ldquoNon-foster matching of a resis-tively loaded vee dipole antenna using operational amplifiersrdquoInstitute of Electrical and Electronics Engineers Transactions onAntennas and Propagation vol 64 no 4 pp 1477ndash1482 2016

[14] HMirzaei and G V Eleftheriades ldquoA resonant printedmonop-ole antenna with an embedded non-foster matching networkrdquoIEEE Transactions on Antennas and Propagation vol 61 no 11pp 5363ndash5371 2013

[15] T K Albee ldquoBroadband VLF loop antenna systemrdquo US Patent3953799 (1976)

[16] M-C TangN Zhu andRWZiolkowski ldquoAugmenting amod-ified egyptian axe dipole antenna with non-foster elements toenlarge its directivity bandwidthrdquo IEEE Antennas and WirelessPropagation Letters vol 12 pp 421ndash424 2013

[17] D Muha S Hrabar I Krois I Bonic A Kiricenko and DZaluski ldquoDesign of microstrip non-foster leaky-wave antennardquoin Proceedings of the 21st International Conference on AppliedElectromagnetics and Communications ICECom 2013 pp 1ndash3hrv October 2013

[18] MM Jacob J Long and D F Sievenpiper ldquoNon-Foster loadedparasitic array for broadband steerable patternsrdquo Institute ofElectrical and Electronics Engineers Transactions on Antennasand Propagation vol 62 no 12 pp 6081ndash6090 2014

[19] A M Elfrgani R Moussounda and R G Rojas ldquoStabil-ity assessment of non-Foster circuits based on time-domainmethodrdquo ETMicrowaves Antenna amp Propagation vol 9 no 15pp 1769ndash1777 2015

[20] T K Albee ldquoSubmarine communication antenna systemrdquo USPatent 3528014 (1966)

[21] C R White J W May and J S Colburn ldquoA variable negative-inductance integrated circuit at UHF frequenciesrdquo IEEEMicrowave and Wireless Components Letters vol 22 no 1 pp35ndash37 2012

[22] S Saadat H Aghasi E Afshari and H Mosallaei ldquoLow-powernegative inductance integrated circuits for GHz applicationsrdquoIEEEMicrowave andWireless Components Letters vol 25 no 2pp 118ndash120 2015

[23] M M Jacob and D F Sievenpiper ldquoGain and Noise Analysis ofNon-Foster Matched Antennasrdquo IEEE Transactions on Anten-nas and Propagation vol 64 no 12 pp 4993ndash5004 2016

[24] L Chao ldquoVLF Communicationsrdquo Bei Jing Tide Press pp 99-100 2008

[25] R S Elliot Antenna Theory and Design John Wiley amp Sons2006

[26] S-M Yim and K K O ldquoDemonstration of a switched resonatorconcept in a dual-band monolithic CMOS LC-tuned VCOrdquo

Proceedings of the Custom Integrated Circuits Conference pp205ndash208 2001

[27] S-J Yun H D Lee K-D Kim S-G Lee and J-K Kwon ldquoAwide-tuning dual-band transformer-based complementaryVCOrdquo IEEE Microwave and Wireless Components Letters vol20 no 6 pp 340ndash342 2010

[28] CEL ldquoNPN RF Transistor NE856 Seriesrdquo 2005

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of


International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Litz coil(10 circles)

1m

1m

25 cm

(a) (b)

Figure 1 (a) Schematic diagram of rectangle loop antenna with shield case (b) Photograph of rectangle loop antenna with shield case (validat a single frequency)

capacitance was matched passively to the antenna and theantennarsquos reactance was canceled by a negative reactancegenerated by a single NFC This matching circuit can onlyfunction at a single frequency or in a small bandwidth asopposed to the whole bandwidth The second obstacle isthe lack of a negative tunable inductor suitable for VLFreceive antenna matching Previous researchers have pre-sented methods in ultrahigh frequency (UHF) [21 22] anddid not address the matching process between the antennasand the tunable NFCsThe third obstacle is the general lack ofresearch on NFC noise and SNR performance Sussman-Fortand Rudish [5] and Jacob and Sievenpiper [23] provided con-flicting results on SNR performance in HFThe present studywas to run a noise and gain test on the receiving system toexamine the NFC networkrsquos SNR performance in VLF

The results presented below suggest that it is feasible tomodify a voltage controlled tunable inductor integrated inNFC for VLF receive antennas Different VLF receive loopantennas can be applied to the designed NFC by switchingeach CMOS ldquoonrdquo or ldquooffrdquo as necessary The noise and gain ofthe passive and non-Foster matching network were alsomeasured to test the actual SNR performance of the VLFreceiving systemAll the datawas analyzed in the small-signalregime (eg receive antennas)

The remainder of this paper is organized as follows Sec-tion 2 presents the design and model method of the receiveloop antenna The design topology of the tunable inductorwhich is integrated in theNFC is presented in Section 31 Sec-tion 32 describes the application of the inductor tunableNFCto the receive antenna in VLF Section 4 presents the gainnoise and SNR of the non-Foster network Section 5 providesa brief conclusion

2 Antenna Design and Model

21 Antenna Design The influence of a noise source near anantenna can be minimized by selecting the proper electric or

magnetic receive antenna and the SNR of the antenna canalso be improved For instance the response of a loop antennawhich has a shield case is 30 dB lower than a same effectiveheight whip antenna under a 0005120582 distance from the staticnoise source (100m at the frequency of 15 kHz) [24]

A 1lowast 1m rectangle loop antennawith a polyvinyl chloride(PVC) pipe shield case was selected as the VLF receiveantenna in this study the loop antenna was designed by litzwire the litz wirewas circled inside a shield pipe and the PVCpipe acts as a supporting function of the litzwireMany circlesof litz wire (99 circles per string 20 strings and 1980 circlesin total) could increase the antennarsquos efficient height Alsoaccording to [24] the signal reception antennas which sub-mains usually use are trailing wire antennas or loop antennasas the trailingwire (around 200m) is too long for experimentso when selecting the type of VLF receive antenna the loopantenna became the first choice As the antenna is woundwith litz wire inside the pipe it is difficult to model it inelectromagnetism (EM) simulation software such as FEKOor HFSS The impedance characteristics of the designedloop antenna were measured and simulated both in practiceand in FEKO the simulation was nearly 120 h long and theVLF results differed substantially

We designed a practical VLF receive loop antenna asthe measurement target Its input impedance characteristicswhich served as parameters for the subsequent design wereobtained by vector network analyzer (VNA) from 15 to30 kHz A schematic diagram of the rectangle loop antenna isshown in Figure 1(a) Figure 1(b) shows a photograph of theantennaThe loop antennarsquos inductancewas determined by (1)as the Litz coil was being wound [24]

119871119886 = 12058311988611989921199012 (1)


S(2 1)

S(1 1)

minus14

minus12

minus10

minus8

S(2

1)(d

B)

minus06

minus04

minus02

0S(1

1)(d

B)


(a)


06496

06498

065

06502

06504

06506

Indu

ctan

ce (m

H)


(b)


Port 1 Port 2

(a) (b)

RlZ0

jXaZ0

jXa

Rr

Rl

Z0

N 1



119898119891 = 1199042119886 (2)




119885119886 = 119877119886 + 119895119883119886 = 119877119903 + 119877119897 + 119895119883119886119877119903 = 119890119903119877119886119877119897 = (1 minus 119890119903) 119877119886

(4)



SW1 SW2 SW3 SW4

L1 L2 L3 L4

L5 L6 L7 L8

(a)

SimMeas






minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

Real

ized

indu

ctan

ce (m

H)

(b)



119873 = radic 1198771199031198850 (5)


119871 = 119883119886(2 lowast 120587 lowast 119891) (6)


119885119886 = 1198850 1 + 119878111 minus 11987811 (7)

3 NFC Design






M4

M1

L2M2

L7

Q1

L1

Q2

L8L4

L5

M3L3

L6

Port1 Port2

L0

L9 = 01 mH

V_DC = 31 V


C3 = 1 uF C4 = 1 uF

R3 = 10 kOhmR1 = 100 Ohm

R6 = 500 Ohm

C1 = 01 uF

C2 = 01 uF

R2 = 100 Ohm

+

++

++

minus

minusminus

minusminus

s

s

s

s

(a)

Port 1 Port 2

Inductorcells

Switches

(b)




The second one is




Port 1 Port 2

+

minus

+

minus

I1 I2


(K gt 0)ZL1 V1


(K gt 0)ZL2V2NFC






282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor



1003816100381610038161003816 (10)





(12)



4 Test and Results





VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S(2 1)

S(1 1)

minus14

minus12

minus10

minus8

S(2

1)(d

B)

minus06

minus04

minus02

0S(1

1)(d

B)


(a)


06496

06498

065

06502

06504

06506

Indu

ctan

ce (m

H)


(b)


Port 1 Port 2

(a) (b)

RlZ0

jXaZ0

jXa

Rr

Rl

Z0

N 1



119898119891 = 1199042119886 (2)




119885119886 = 119877119886 + 119895119883119886 = 119877119903 + 119877119897 + 119895119883119886119877119903 = 119890119903119877119886119877119897 = (1 minus 119890119903) 119877119886

(4)



SW1 SW2 SW3 SW4

L1 L2 L3 L4

L5 L6 L7 L8

(a)

SimMeas






minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

Real

ized

indu

ctan

ce (m

H)

(b)



119873 = radic 1198771199031198850 (5)


119871 = 119883119886(2 lowast 120587 lowast 119891) (6)


119885119886 = 1198850 1 + 119878111 minus 11987811 (7)

3 NFC Design






M4

M1

L2M2

L7

Q1

L1

Q2

L8L4

L5

M3L3

L6

Port1 Port2

L0

L9 = 01 mH

V_DC = 31 V


C3 = 1 uF C4 = 1 uF

R3 = 10 kOhmR1 = 100 Ohm

R6 = 500 Ohm

C1 = 01 uF

C2 = 01 uF

R2 = 100 Ohm

+

++

++

minus

minusminus

minusminus

s

s

s

s

(a)

Port 1 Port 2

Inductorcells

Switches

(b)




The second one is




Port 1 Port 2

+

minus

+

minus

I1 I2


(K gt 0)ZL1 V1


(K gt 0)ZL2V2NFC






282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor



1003816100381610038161003816 (10)





(12)



4 Test and Results





VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










SW1 SW2 SW3 SW4

L1 L2 L3 L4

L5 L6 L7 L8

(a)

SimMeas






minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

Real

ized

indu

ctan

ce (m

H)

(b)



119873 = radic 1198771199031198850 (5)


119871 = 119883119886(2 lowast 120587 lowast 119891) (6)


119885119886 = 1198850 1 + 119878111 minus 11987811 (7)

3 NFC Design






M4

M1

L2M2

L7

Q1

L1

Q2

L8L4

L5

M3L3

L6

Port1 Port2

L0

L9 = 01 mH

V_DC = 31 V


C3 = 1 uF C4 = 1 uF

R3 = 10 kOhmR1 = 100 Ohm

R6 = 500 Ohm

C1 = 01 uF

C2 = 01 uF

R2 = 100 Ohm

+

++

++

minus

minusminus

minusminus

s

s

s

s

(a)

Port 1 Port 2

Inductorcells

Switches

(b)




The second one is




Port 1 Port 2

+

minus

+

minus

I1 I2


(K gt 0)ZL1 V1


(K gt 0)ZL2V2NFC






282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor



1003816100381610038161003816 (10)





(12)



4 Test and Results





VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










M4

M1

L2M2

L7

Q1

L1

Q2

L8L4

L5

M3L3

L6

Port1 Port2

L0

L9 = 01 mH

V_DC = 31 V


C3 = 1 uF C4 = 1 uF

R3 = 10 kOhmR1 = 100 Ohm

R6 = 500 Ohm

C1 = 01 uF

C2 = 01 uF

R2 = 100 Ohm

+

++

++

minus

minusminus

minusminus

s

s

s

s

(a)

Port 1 Port 2

Inductorcells

Switches

(b)




The second one is




Port 1 Port 2

+

minus

+

minus

I1 I2


(K gt 0)ZL1 V1


(K gt 0)ZL2V2NFC






282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor



1003816100381610038161003816 (10)





(12)



4 Test and Results





VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











282624 3014 201816 22Frequency (kHz)

08

10

12

14

16

18

20

22

Stab

le fa

ctor



1003816100381610038161003816 (10)





(12)



4 Test and Results





VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










VAR1EqnVar

OptimGoal2

GOAL

OptimGoal1

GOAL

OptimType = Genetic

OPTIM

S2P

21Ref Term2Term1

Loop antenna model

+

minus

+

minus



C2

C2 = 90 o

C = 514 nFF = 225 kHz


C1 = 500 o


VNA

PassiveNFCmatching

Antenna

1

2

(a)

VNA


1

2

La

Ra

(b)


VNA

Loop antenna

NFC

DC power

S11

(a)

VNA

NFC

Antenna model

DC power

S21

(b)






minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus25

minus20

minus15

minus10

minus5

S11

(dB)

0

5




(a)

minus25

minus20

minus15

minus10

minus5

0

5

S21

(dB)




(b)



Non-Foster matching

Antenna


Passivematching

Antenna

Preamplifier

Preamplifier

= 4 dB

= 4 dB













Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Passive noise

minus130

minus120

minus110

minus100

minus90

Noi

se p

ower

(dBm

Hz)

minus69

minus685

minus68

minus675

minus67

Real

ized

gai

n (d

Bm)

(a)



minus8

minus6

minus4

minus2

0

2

Gai

n an

d SN

R im

prov

emen

t (dB

)

(b)




5 Conclusion





References
































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Non-Foster Matching Circuit Design via Tunable Inductor