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International Journal of Antennas and Propagation

Volume 2013 (2013), Article ID 531419, 7 pages

http://dx.doi.org/10.1155/2013/531419

## Non-Foster Impedance Wideband Matching Technique for Electrically Small Active Antenna

College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

Received 28 July 2013; Accepted 12 September 2013

Academic Editor: Dau-Chyrh Chang

Copyright © 2013 Wenxing Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper investigates a non-Foster wideband circuit matching technique for an electrically small antenna (ESA). By introducing a negative impedance convertor into an active network, the active network can obtain an equivalent input gain at input port to improve gain, sensitivity and output ratio of signal to noise. In addition, it also increases the effective height of active antenna. The experimental results have verified the proposed method by using a 100 KHz–30 MHz wideband active receiving monopole antenna.

#### 1. Introduction

With miniaturization of radio equipment, the broadband and compact antenna becomes more demanded for broadband communication equipment. As a well-known fact, an electrically small antenna usually presents a high radiation quality factor , and its impedance is characterized by a large reactance and a small radiation resistance. The gain bandwidth and efficiency of an electrically small antenna with a passive matching network are limited. Traditional active receiving antenna is composed of a field effect transistor (FET) with a high input impedance to achieve a wideband property [1]. However, due to suffering from the FET input capacitance an active network cannot achieve desired effective height.

The electrically small receiving antenna with Non-Foster matching can tickle the gain-bandwidth limitation, which was proposed by Harris, Myers, and Perry [2, 3]. This topic has drawn more attention for many years [4–12], and the significant achievements has made on this topic [8]. Though the existing techniques of electrically small antenna with non-Foster matching [9] network can obtain a good performance. However, it requires a relatively complex circuit. In this paper, we start with theoretical analysis of electrically small active receiving antenna with non-Foster matching network. At the input port of active network, we can get a negative equivalent input capacitance to obtain an equivalent input gain, which can increase gain of active antenna, sensitivity, and signal to noise ratio (SNR). The experimental results are employed to validate the proposed technique.

#### 2. Non-Foster Matching Analysis of Electrically Small Antenna

##### 2.1. Small Antenna

An electrically small antenna presents a high radiation quality factor and an impedance with a large reactance and a small radiation resistance. The theoretical minimum of an electrically small antenna for a single mode is expressed as follows: where is wave number in free space and is radius of the smallest sphere enclosing the entire antenna. It is observed from (1) that an electrically small antenna has a higher quality factor. It is a well-known fact that the traditional passive matching antenna has a relatively narrow bandwidth.

The equivalent circuit for an electrically small monopole antenna consists of components of reactance , radiation resistance , and loss of resistance . The loss of resistance is usually ignored due to its low level. Theoretically, the radiation resistance and reactance for a monopole antenna are expressed as follows: where and are the physical length and radius of monopole, respectively. The monopole is 1,000 mm long and its radius is 5 mm. The real and imaginary parts of the monopole antenna input impedance are shown in Figure 1.

##### 2.2. Negative Impedance Convertor Analysis

The traditional active antenna is composed of an electrically small antenna and an active element. This paper investigates the monopole antenna that is directly connected to an FET amplifier, as shown in Figure 2.

The electric field generated at the antenna input port can be expressed as , where is an electric field strength, and is an effective height. The equivalent capacitance and FET input capacitance of the monopole antenna form a capacitive divider voltage. The input voltage of amplifier is expressed as follows: where is frequency independent and its bandwidth is dependent on the amplifier property. If increases or decreases, the input voltage may approach to the maximal value. value, limited by an electronic device, is hard to decrease. Increasing the antenna height can degrade unexpectedly. Non-Foster impendence from the negative impedance convertor using a positive feedback capacitor and amplifier can help reduce capacitance of the amplifier, and furthermore get the negative equivalent input capacitance of active network.

The antenna equivalent circuit of an electrically small antenna along with a negative impedance convertor circuit [11] is presented in Figure 3.

In Figure 3, indicates gain of the amplifier voltage; represents the active antenna load impedance; and denotes the positive feedback capacitor.

By analyzing the circuit in Figure 3, we can get a set of equations as follows:

The active network equivalent input voltage gain is given in the following format:

The voltage gain of an active antenna is obtained as follows:

##### 2.3. Equivalent Input Gain Analysis

We use the formulation to express the negative equivalent capacitance at input port of an active network of a negative impedance convertor. Next, we consider the equivalent input capacitance of an active network for different combinations of and . There exist three possibilities: (1) ; (2) ; and (3) . We discuss the relationship between and for the three cases [12].

(1) . For in (5), we have , implying that the antenna source voltage cannot be transmitted to the active network and the antenna gain is larger than the traditional active antennas. It is worthwhile to mention that the equivalent input gain in this case is less than 1.

(2) . For in (5), we have ; namely, the active network input voltage is equal to the antenna source voltage, which implies that the input capacitance of the amplifier equals to 0 [11]. This is considered as the non-Foster matching case and its application is limited to improve the antenna gain and SNR [9].

(3) . For in (5), we have , which allows us to get a negative equivalent capacitance at input port of the active network. The active network input signal is larger than the received signal, which is similar to the enhanced non-Foster matching and useful for improving the efficiency of the antenna gain and SNR [9].

##### 2.4. Stability Analysis

Since the principal ingredient of negative impedance convertor is a positive feedback circuit, we must carry out a stability analysis of the active antenna to derive a stability criterion. Using (5), we can derive a stability condition; for example, . Considering the condition of negative impedance convertor, must be satisfied with both and ; namely,

If an active antenna works in the status , for , we have

Equation (8) defines the stability criterion for an active antenna, which implies that must be satisfied with either (7) or (8) in the working frequency band. Outside the frequency band, it must be satisfied with the following criterion:

Equations (8) and (9) are the stable criterions that must be satisfied with designing an active receiving antenna.

##### 2.5. Sensitivity Analysis

Sensitivity is an important indicator for an active receiving antenna, which can be expressed as the equivalent noise field strength of the inherent noise. If is the inherent noise of an active receiving antenna, its equivalent noise field strength can be expressed as [11]

For three cases , , and , is taken to be , , and , respectively. From (10), we have It is obvious that the highest active receiving antenna sensitivity is reached for .

#### 3. Design of Active Receiving Antenna

##### 3.1. Design Considerations

The design technique described in the last section is implemented in an active receiving antenna design in the shortwave band. The length and radius of the monopole antenna are 1,000 mm and 5 mm, respectively.

It is important to investigate the receiving sensitivity and nonlinear distortion performance in an active antenna design. When the signal interference of a shortwave antenna is severe, the nonlinear distortion performance becomes especially important and is usually interfered with the second- and third-order intermodulation distortions (IMD) performance. Increasing depth of an active network negative feedback can improve the active antenna nonlinear distortion, and the deeper negative feedback can improve the nonlinear distortion [13]. System noise is closely related to the primary gain. The higher gain of the first level amplifier will improve the system noise and sensitivity. The IMD performance degrades with the cascaded operational amplifiers. With the compromise of parameters, an active receiving antenna with a low noise amplifier and negative impedance converter is shown in Figure 4.

The active antenna in this paper is based on the operational amplifier OPA657, a product of Texas Instruments, due to their better IMD, low noise, JFET-input, high dynamic range, and high gain bandwidth performances. The equivalent circuit of the active receiving antenna is shown in Figure 5.

##### 3.2. Gain and Negative Impedance Analysis

The antenna equivalent capacitance is 15 pF and the amplifier voltage factor is . For the resistance parameters shown in Figure 5, the amplifier voltage factor is 4. The operational amplifier voltage gain is expressed in the following format:

The operational amplifier voltage gain is 6 dB for a 50-ohm load impedance.

The active network input capacitance in Figure 5 consists of input capacitance of the amplifier, electromagnetic pulse protection device equivalent capacitance and PCB distributed capacitance. In the absence of negative impedance converter, the active antenna gain is less than 6 dB. By adjusting the feedback capacitance of negative impedance converter, we can obtain an equivalent negative capacitance at the input port of active network and an equivalent input gain, which can achieve an active antenna gain greater than 6 dB.

##### 3.3. Filter Design

Active network bandwidth is determined by the operational amplifier. 200 MHz bandwidth can be achieved and the amplifier voltage factor is 4. The broad bandwidth helps improve the amplifier linearity and bandwidth.

A 13-order Butterworth low-pass filter is shown in Figure 6. To get a flat gain pattern inside 30 MHz bandwidth, 3 dB bandwidth has been designed for about 40 MHz. The simulated -parameters are shown in Figure 7.

#### 4. Test and Analysis of Active Antenna

The prototype of the active network is shown in Figure 8 and the capacitance of antenna impedance is 15 pF. We investigate the performance of the active antenna below.

##### 4.1. Gain Test

Adjusting positive feedback capacitance can change the equivalent input capacitance of an active network. The variation of active network voltage gain with frequency is shown in Figure 9.

For , the active receiving antenna voltage gain is less than 6 dB in a 50-ohm load impedance. The voltage gain is 6 dB for . However, the active receiving antenna voltage gain is larger than 6 dB for . When the equivalent input capacitance of an active network increases, the equivalent input voltage gain of the active network also increases. Gain of the active receiving antenna is near 12 dB for pF, and the equivalent input gain is 6 dB. Gain of the active receiving antenna is near 18 dB for pF, and the equivalent input gain is 12 dB. When the equivalent input capacitance is close to , the voltage gain fluctuates considerably, indicating that the antenna stability deteriorates and should not be chosen too close to .

##### 4.2. Voltage Standing Wave Ratio

The voltage standing wave ratio (VSWR) of the active antenna is shown in Figure 10, and it is observed from the figure that VSWR in 100 kHz–30 MHz is less than 1.2, which can be in a good match to the receiver.

##### 4.3. Noise Measurement

In the shortwave band, the ambient noise is more severe. The noise figure of active receiving system indicates the active receiving antenna noise performance. The noise of the active receiving system is expressed where is the ambient noise factor and is the noise factor of the active receiving antenna. Practically, the noise factor of the active receiving system is the ratio of the output SNR of the active antennas to the input SNR; and is usually less than 2.

The noise factor of active receiving system is expressed as where is the output voltage generated by the active antenna noise, and is the output voltage generated by the ambient noise [14].

From (14), we can develop a simple but efficient method to measure the noise factor of an active antenna system, namely, the inherent noise voltage in an electromagnetic mask room, the noise output voltage in open free space, and the ambient noise voltage . Substituting them into (14), we obtain

If the testing receiver noise cannot be ignored, we can measure the inherent noise voltage of the receiver in an electromagnetic mask room. We can measure the inherent noise voltages first in an electromagnetic mask room and the noise output voltage of the active antenna second in free space. Then, we can get

Using the strategy above, the measurement results are shown in Figure 11, which demonstrate that the ratio of noise of the active receiving system to the noise figure is less than 1.1. The designed antenna in this environment shows a good performance.

##### 4.4. Intermodulation Distortion Measurement

Intermodulation distortion measurement is a very important factor in the broadband active receiving antenna. A typical measurement configuration for IMD in an active receiving antenna is shown in Figure 12.

Intermodulation attenuation of an active receiving antenna is related to the output signal power. The measurement of the second- and third-order intermodulation attenuation is measured for the same inputs and −7.0 dBm of the mutual interference signal output, as shown in Tables 1 and 2.

#### 5. Conclusions

In this paper, we present an analysis and design of an active receiving antenna utilizing negative impedance convertor. We use a low noise operational amplifier to realize the design of active receiving antenna in 100 KHz–30 MHz frequency band. Experimental results demonstrate the negative impedance converter that can improve gain, receiving system sensitivity, and broadband characteristic. The performance of active antenna is closely related to semiconductor technology, and the active antenna design will become more attractive.

#### Conflict of Interests

This paper does not have a direct financial relation with the commercial identities mentioned in the paper.

#### Acknowledgment

This paper is supported by the Fundamental Research Funds for the Central Universities.

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