1

1.5 GHz Negative Impedance Converters

O.O. Tade, P. Gardner and P.S. Hall

School of Electronic, Electrical and Computer Engineering,

University of Birmingham, UK. B15 2TT

oot850@bham.ac.uk

Keywords: Cognitive radio, Electrically small antenna, Non-Foster

matching networks,.

Abstract

The need for small antenna with wide instantaneous

bandwidth is vital in mobile Cognitive radio nodes /

transceivers. The fundamental limit of small antennas is a

problem which passive matching cannot solve. However, non-

Foster matching provides a solution to this problem. In this

paper, we show a negative impedance converter that provides

a negative capacitor up to 1.5GHz. This is the highest

frequency report to date. The negative capacitor can help

increase the Q of antennas beyond what is achievable with

passive matching.

1 Introduction

Cognitive radios are currently generating a lot interest

because of the promise of access to a wide range of

underutilised RF spectrum. This access comes with some pre-

requisites, one of which is that the CR node must be able to

detect a licensed user, known as Primary user (PU), within

two (2) seconds of the PU becoming active. To achieve this

objective, the CR nodes need to carry out spectrum sensing.

Spectrum sensing can be achieved by using wide band RF

front-ends which require wideband antennas [1] or a wide-

tuning antenna. Current trends suggest that CR nodes would

need to be mobile and possibly handheld hence the need for

small antennas. Small antennas are usually narrow band and

would require some form of external matching. Passive

matching limits the bandwidth because it involves resonating

the reactive part of the antenna. Complete cancellation of the

reactive part of an antenna is only possible over very narrow

bandwidths when using passive (Foster) elements [2]. This

implies that antennas would have to be tuneable to cover wide

bandwidth. Using tuneable antennas for spectrum sensing

would not take advantage of the advances made in digital

signal processing (DSP) where concurrent signal processing

can be done at baseband [3]. To achieve wideband small

antennas, there is the need for non-Foster elements. These

elements have a negative reactance slope and this feature

enables non-Foster elements to cancel the reactance of an

antenna continuously over a wide bandwidth [2].

A means of achieving non-Foster element is through the use

of Negative Impedance Converters (NIC). An NIC is an

active two port network which inverts whatever impedance is

connected to its other port Fig. 1. Previous attempts at making

NIC based matching networks include [2] which matched a

six (6) inch antenna from 20MHz to 120MHz. Ref [4]

matched a meta-material based antenna which provided a

better than 10dB return loss between 450MHz and 500MHz

with a top frequency of 500MHz. Other attempts either show

either analytical or simulated results.

Figure 1: An idealized NIC

2 NIC Design

We have been able to design and build an NIC which has a

top frequency of 1.5GHz, which is the highest reported so far.

The NIC was fabricated using Linvill’s model [5]. The

Linvill’s model consists of two transistors. The reactive

element to invert is connected between the collectors of the

transistor. The base of one transistor is connected to the

collector of the second transistor and this forms the feedback

path. The two emitters form the terminals of the NIC. The

Linvill’s schematic is shown in Fig. 2a. It is realized as a (50

X 50) mm2 double layer structure with a common ground

plane between the two layers as shown in fig. 2b. The two

layered structure approach was chosen because it provides the

shortest feedback path. The feedback length is critical in

ensuring stability. Vias are used to connect the two layers of

the structure. The substrate used in the fabrication is Taconic

TLY-5 with thickness of 1.57mm, dielectric constant of 2.2

and loss tangent of 0.0009. On the top layer, fig. 2c, are the

transistors, the capacitor to invert and the DC bias network.

The reverse or bottom layer, fig. 2d, has the feedback path.

The transistor is a SOT23 packaged NXP BFS 17 transistor

biased at 5V, 20mA. The capacitor to invert is an AVX 3.9pF

and it is connected between the two transistors as shown in

fig. 2c. There are input and output coplanar waveguide

(CPW) transmission lines between the emitter of the

transistors and the 50Ω measurement ports.

As negative capacitors are inherently unstable therefore it is

necessary to add positive capacitors in between the

measurement ports and the NIC. This ensures that the total

capacitance seen from either of the measurement ports is

always positive. 10Ω resistors are also added between the

2

(a)

Bias

Lines

Capacitor

to invert

Via

hole

CapacitorResistor Transistor

A

B

Transmission Line

Common

ground-planeVia

(b)

DC blocking

Capacitor

Via

hole

(c) (d)

Fig 2: The layout of the NIC (a) Linvill’s NIC schematic (b) Cross-sectional view (c) Top view and (d) Reverse view

measurement port and the NIC to further ensure stability by

providing resistive damping. The NIC exists between points

A and B (fig. 2c). Other components after these points are

added to make the NIC measureable as a standalone structure.

The performance of the NIC alone is found by de-embedding

it from the measured S – parameters of the structure.

3 Measurement results

The structure shown in Fig. 2 has been built and measured.

The measured S11and S22 results are shown in Fig.3. Fig.3

also shows the NIC performance after the effects of the

transmission line, stabilizing resistors and capacitors have

been de-embedded from the measured result. The plots shown

in Fig. 3 below, shows non-Foster performance after de-

embedding. It can be seen that the locus of S11 and S22 plots

rotate anticlockwise with increase in frequency between

595MHz and 1.5GHz. De-embedding entails removing the

effects of all the additional elements (resistor and capacitor)

and the transmission lines between the measurement ports and

points A and B (Fig. 2c). A plot of the resistance and

reactance seen from points A and B is shown in fig. 4. The

reactance plot shows a negative slope which indicates the

presence of a negative reactive element.

Fig 3: De-embedded Measured S parameter of NIC.

CAPID=C1C=1 pF

C

B

E

1

2

3

GBJT3ID=GP1

C

B

E

1

2

3

GBJT3ID=GP2

PORTP=2Z=50 Ohm

PORTP=1Z=50 Ohm

0 1.0

1.0

-1.0

10.0

10.0

-10.0

5.0

5.0

-5.0

2.0

2.0

-2.0

3.0

3.0

-3.0

4.0

4.0

-4.0

0.2

0.2

-0.2

0.4

0.4

-0.4

0.6

0.6

-0.6

0.8

0.8

-0.8

Swp Max

1500MHz

Swp Min

400MHz

1500 MHzr 14.8499x -3.63755

595 MHzr 0.202597x 0.0952731

S(1,1)De-embedded Measured NIC

S(2,2)De-embedded Measured NIC

3

Fig 4: Impedance Graph of de-embedded NIC

4 Conclusion

We have presented a double sided two-port NIC which shows

a capability of non-Foster behaviour up to 1.5GHz, which is

the highest reported. This NIC circuit can be used as a

matching network or part of a broadband matching network

for small antenna. There is a need for proper stability analyses

as stability is a major challenge with negative elements and

NICs.

References

[1] I. F. Akyildiz, et al., "A survey on spectrum

management in cognitive radio networks,"

Communications Magazine, IEEE, vol. 46, pp. 40-

48, 2008.

[2] S. E. Sussman-Fort and R. M. Rudish, "Non-Foster

Impedance Matching of Electrically-Small

Antennas," Antennas and Propagation, IEEE

Transactions on, vol. 57, pp. 2230-2241, 2009.

[3] H. R. Myler, et al., "A concurrent processing

approach for software defined radio baseband

design," in Technical, Professional and Student

Development Workshop, 2005 IEEE Region 5 and

IEEE Denver Section, 2005, pp. 20-24.

[4] H. Mirzaei and G. V. Eleftheriades, "A wideband

metamaterial-inspired compact antenna using

embedded non-Foster matching," in Antennas and

Propagation (APSURSI), 2011 IEEE International

Symposium on, 2011, pp. 1950-1953.

[5] J. G. Linvill, "Transistor Negative-Impedance

Converters," Proceedings of the IRE, vol. 41, pp.

725-729, 1953.

400 900 1400 1500

Frequency (MHz)

-100

-50

0

50

Re

acta

nce

(o

hm

s)

0

20

40

60

Re

sis

tan

ce

(o

hm

s)

Im(Z(1,1)) (L)De-embedded Measured NIC

Im(Z(2,2)) (L)De-embedded Measured NIC

Re(Z(1,1)) (R)De-embedded Measured NIC

Re(Z(2,2)) (R)De-embedded Measured NIC