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

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 𝑄, 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 𝑄 and an impedance with a large reactance and a small radiation resistance. The theoretical minimum 𝑄 of an electrically small antenna for a single mode is expressed as follows: 1𝑄=𝑘³𝑎³+1,𝑘𝑎 (1) where 𝑘 is wave number in free space and 𝑎 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 𝑗𝑋_𝑎, radiation resistance 𝑅_𝑟, and loss of resistance 𝑅_𝐿. The loss 𝑅_𝐿 of resistance is usually ignored due to its low level. Theoretically, the radiation resistance and reactance for a monopole antenna are expressed as follows: 𝑅_𝑟=40𝜋²ℎ𝜆²,𝑋_𝑎ℎ=601−ln𝑏ℎ⋅cot2𝜋𝜆, (2) where ℎ and 𝑏 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.

Figure 1 

Real and imaginary parts of input impedance of the monopole antenna.

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.

Figure 2 

Equivalent circuit of a traditional active antenna.

The electric field generated at the antenna input port can be expressed as 𝑉_𝑆=𝐸ℎ_eff, where 𝐸 is an electric field strength, and ℎ_eff is an effective height. The equivalent capacitance 𝐶_𝑎 and FET input capacitance 𝐶_𝑖 of the monopole antenna form a capacitive divider voltage. The input voltage of amplifier is expressed as follows: 𝑉_𝑖=𝑉_𝑠𝐶_𝑎𝐶_𝑎+𝐶_𝑖, (3) where 𝑉_𝑖 is frequency independent and its bandwidth is dependent on the amplifier property. If 𝐶_𝑎 increases or 𝐶_𝑖 decreases, the input voltage may approach to the maximal value. 𝐶_𝑖 value, limited by an electronic device, is hard to decrease. Increasing the antenna height can degrade 𝐶_𝑎 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.

Figure 3 

Equivalent circuit of a non-Foster matching electrically small antenna.

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

By analyzing the circuit in Figure 3, we can get a set of equations as follows: 𝐼_𝑎=𝑗𝜔𝐶_𝑎𝑉_𝑠−𝑉_𝑖,𝐼_𝑖=𝑗𝜔𝐶_𝑖𝑉_𝑖,𝐼_𝑓=𝑗𝜔𝐶_𝑁𝑉_𝑜−𝑉_𝑖,𝐼_𝑖=𝐼_𝑎+𝐼_𝑓,𝑉_𝑜=𝐴_𝑣𝑉_𝑖. (4)

The active network equivalent input voltage gain is given in the following format: 𝑉_𝑖𝑉_𝑠=𝐶_𝑎𝐶_𝑎+𝐶_𝑖+1−𝐴_𝑉𝐶_𝑁. (5)

The voltage gain of an active antenna is obtained as follows: 𝑉_𝑜𝑉_𝑠=𝐶_𝑎𝐶_𝑎+𝐶_𝑖+1−𝐴_𝑉𝐶_𝑁⋅𝐴_𝑉. (6)

2.3. Equivalent Input Gain Analysis

We use the formulation 𝐶^′_𝑁=(1−𝐴_𝑉)𝐶_𝑁 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 𝐶=𝐶_𝑖+(1−𝐴_𝑁)𝐶_𝑁 for different combinations of 𝐴_𝑉 and 𝐶_𝑁. There exist three possibilities: (1) 𝐶>0; (2) 𝐶=0; and (3) 𝐶<0. We discuss the relationship between 𝑉_𝑖 and 𝑉_𝑆 for the three cases [12].

(1) 𝐶>0. For |𝐶^′_𝑁|<𝐶_𝑖 in (5), we have 𝑉_𝑖<𝑉_𝑆, 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) 𝐶=0. For |𝐶^′_𝑁|=𝐶_𝑖 in (5), we have 𝑉_𝑖=𝑉_𝑆; 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) 𝐶<0. For |𝐶^′_𝑁|>𝐶_𝑖 in (5), we have 𝑉_𝑖>𝑉_𝑆, 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, 𝐶_𝑎+𝐶_𝑖+(1−𝐴_𝑉)𝐶_𝑁≠0. Considering the condition of negative impedance convertor, 𝐴_𝑉 must be satisfied with both 𝐴_𝑣>1 and 𝐶_𝑎+𝐶_𝑖+(1−𝐴_𝑉)𝐶_𝑁>0; namely, 1<𝐴_𝑉𝐶<1+^𝑎+𝐶_𝑖𝐶_𝑁. (7)

If an active antenna works in the status 𝑉_𝑖>𝑉_𝑆, for −𝐶_𝑎<𝐶<0, we have 𝐶1+^𝑖𝐶_𝑁<𝐴_𝑉𝐶<1+^𝑎+𝐶_𝑖𝐶_𝑁. (8)

Equation (8) defines the stability criterion for an active antenna, which implies that 𝐴_𝑉 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: 𝐴_𝑉𝐶<1+^𝑎+𝐶_𝑖𝐶_𝑁. (9)

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 𝑉²_𝑎 is the inherent noise of an active receiving antenna, its equivalent noise field strength 𝑒²_𝑎 can be expressed as [11] 𝑒²_𝑎=𝑉²_𝑎𝐶_𝑎+𝐶_𝑖+1−𝐴_𝑉𝐶_𝑁/𝐶_𝑎ℎ_eff=𝑉²_𝑎𝐶_𝑎+𝐶/𝐶_𝑎ℎ_eff. (10)

For three cases 𝐶>0, 𝐶=0, and 𝐶<0, 𝑒²_𝑎 is taken to be 𝑒²_𝑎1, 𝑒²_𝑎2, and 𝑒²_𝑎3, respectively. From (10), we have 𝑒²_𝑎1>𝑒²_𝑎2>𝑒²_𝑎3. (11) It is obvious that the highest active receiving antenna sensitivity is reached for 𝐶<0.

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.

Figure 4 

Block diagram of the active antenna.

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.

Figure 5 

Schematic diagram of equivalent circuit for active receiving antenna.

3.2. Gain and Negative Impedance Analysis

The antenna equivalent capacitance is 15 pF and the amplifier voltage factor is 𝐺=1+𝑅₁/𝑅₂. 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: 𝐺_𝑎1=20log2𝑅1+²𝑅₃dB. (12)

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

The active network input capacitance 𝐶₅ 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 𝐶_𝑁 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 𝑆-parameters are shown in Figure 7.

Figure 6 

Schematic diagram of the low-pass filter.

Figure 7 

𝑆-parameters of the low-pass filter.

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.

Figure 8 

Photograph of the active network.

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.

Figure 9 

Gain variation of the active receiving antenna with frequency.

For 𝐶>0, the active receiving antenna voltage gain is less than 6 dB in a 50-ohm load impedance. The voltage gain is 6 dB for 𝐶=0. However, the active receiving antenna voltage gain is larger than 6 dB for 𝐶<0. When the equivalent input capacitance |𝐶| of an active network increases, the equivalent input voltage gain of the active network 𝑉_𝑖/𝑉_𝑆 also increases. Gain of the active receiving antenna is near 12 dB for 𝐶=−3.7 pF, and the equivalent input gain is 6 dB. Gain of the active receiving antenna is near 18 dB for 𝐶=−7.5 pF, and the equivalent input gain is 12 dB. When the equivalent input capacitance |𝐶| is close to 𝐶_𝑎, the voltage gain fluctuates considerably, indicating that the antenna stability deteriorates and |𝐶| should not be chosen too close to 𝐶_𝑎.

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.

Figure 10 

VSWR variation of the active antenna with frequency.

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 𝐹_𝑠𝐹=1+^𝑎−1𝐹_𝐴, (13) where 𝐹_𝐴 is the ambient noise factor and 𝐹_𝑎 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 𝐹_𝑠 is usually less than 2.

The noise factor of active receiving system is expressed as 𝐹_𝑠𝑉=1+^2𝑎𝑉²_𝐴, (14) where 𝑉_𝑎 is the output voltage generated by the active antenna noise, and 𝑉_𝐴 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 𝑉_𝑎 in an electromagnetic mask room, the noise output voltage 𝑉_𝑜 in open free space, and the ambient noise voltage 𝑉_𝐴. Substituting them into (14), we obtain 𝐹_𝑠𝑉=1+^2𝑎𝑉²_𝑜−𝑉²_𝑎. (15)

If the testing receiver noise cannot be ignored, we can measure the inherent noise voltage 𝑉_Ins of the receiver in an electromagnetic mask room. We can measure the inherent noise voltages 𝑉₁=𝑉_𝑎+𝑉_Ins first in an electromagnetic mask room and the noise output voltage 𝑉₂=𝑉_𝑜+𝑉_Ins of the active antenna second in free space. Then, we can get 𝐹_𝑠𝑉=1+¹−𝑉_Ins²𝑉₂−𝑉_Ins²−𝑉₁−𝑉_Ins². (16)

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.

Figure 11 

Ratio of 𝐹𝑠 to the noise factor variation with frequency.

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.

Figure 12 

Intermodulation distortion measurement configuration.

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.

Table 1 

Second order IMD result.

Table 2 

Third order IMD result.

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.