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

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## Abstract

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## Featured Application

**Miniaturized broadband antennas for wireless communication devices**

## Abstract

## 1. Introduction

## 2. Non-Foster Circuit Design

#### 2.1. Characteristics of Electrically Small Antenna

#### 2.2. Non-Foster Circuit Design

_{ref}) of the NFC was set to 6 pF considering the monopole’s capacitance. The values of inductors (L

_{G}, L

_{D}, L

_{S}) and resistors (R

_{G}, R

_{D}, R

_{s}) connected to the gate, drain, and source of the transistors should be carefully chosen to ensure the wideband stability criterion. As the value of the inductor increases, its self-resonant frequency (SRF) decreases, adversely affecting the NFC stability [16]. The resistor values are also important since the wrong selection can lead to a generation-negative resistance that goes against the stability condition [17]. To reduce the loop gain of the transistors for stability, R

_{Stab}and C

_{Stab}are set as 51 Ω, 1 pF, respectively. The gate voltage (V

_{GG}), drain voltage (V

_{DD}), and drain current of the designed circuit are 1.8 V, 5.7 V, and 4 mA, respectively.

#### 2.3. Non-Foster Circuit Stability Check

_{Ant}| > |Z

_{NFC}|,

_{Ant}| and |Z

_{NFC}| are the magnitudes of the antenna and NFC impedance. This condition must be satisfied throughout the frequency band of interest where the NFC generates the negative impedance. Figure 5 shows |Z

_{Ant}| > |Z

_{NFC}| in the frequency range of 50–500 MHz for the proposed NFC. It is observed that the OCS criterion in (1) is satisfied.

## 3. Fabrication and Measurement of Non-Foster Circuit

#### 3.1. Measurement of Reflection Coefficient

#### 3.2. Measurement of Signal-to-Noise Ratio

_{ESA}, N

_{ESA}) without the NFC and (S

_{ESA+NFC}, N

_{ESA+NFC}) with the NFC, respectively. With them, the SNR enhancement due to the NFC can be calculated by

## 4. Conclusions

_{11}< –10 dB bandwidth after applying the NFC was 60–400 MHz, broad enough to cover several VHF and UHF communication bands with an antenna length less than 10 cm. The received power measurement also showed promising results that are more than 17 dB of improvement after applying the NFC. However, the NFC accompanies a highly fluctuating noise power of 7 to 14 dB that adversely affects the SNR.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Antenna reactance cancellation using (

**a**) passive components which follow the Foster’s reactance theorem. (

**b**) Negative reactance generated by the non-Foster circuit matching technique.

**Figure 4.**Simulation results of the non-Foster circuit: (

**a**) Smith chart of the reflection coefficient. (

**b**) Negative capacitance versus frequency.

**Figure 5.**A comparison of the magnitudes of the antenna and non-Foster circuit impedance to check the open-circuit stability criterion.

**Figure 6.**The transient responses of non-Foster circuits: (

**a**) Examples of stable and unstable transient responses. (

**b**) The transient response of the proposed non-Foster circuit.

**Figure 8.**The measurement of the reflection coefficient of the monopole and non-Foster circuit assembly: (

**a**) A picture of the fabricated non-Foster circuit connected to the monopole. (

**b**) The measured reflection coefficient with and without the non-Foster circuit.

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

**Figure 10.**The power measurement data with and without the non-Foster circuit: (

**a**) received power and (

**b**) noise power.

**Table 1.**Optimized values of passive components in Figure 3.

Parameter | Value | Parameter | Value |
---|---|---|---|

Z_{ref} | 6 pF | R_{S} | 600 Ω |

L_{G} | 1 uH | R_{Stab} | 51 Ω |

L_{D} | 1 uH | C_{Stab} | 1 pF |

L_{S} | 4.7 uH | C_{G} | 510 pF |

R_{G} | 1.1 KΩ | C_{in} | 100 pF |

R_{D} | 1.1 KΩ | C_{out} | 510 pF |

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**MDPI and ACS Style**

Lee, Y.-H.; Cho, S.-y.; Chung, J.-Y. SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit. *Appl. Sci.* **2020**, *10*, 4464.
https://doi.org/10.3390/app10134464

**AMA Style**

Lee Y-H, Cho S-y, Chung J-Y. SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit. *Applied Sciences*. 2020; 10(13):4464.
https://doi.org/10.3390/app10134464

**Chicago/Turabian Style**

Lee, Yong-Hyeok, Sung-yong Cho, and Jae-Young Chung. 2020. "SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit" *Applied Sciences* 10, no. 13: 4464.
https://doi.org/10.3390/app10134464