# SNR Enhancement of an Electrically Small Antenna Using a Non-Foster Matching Circuit
## 1 Introduction  
The demand for miniaturized communication systems has tremendously increased for many applications such as mobile devices, medical wearables, military radios and vehicles, etc. One of the key components that prohibit the miniaturization is an antenna because of its physical length (or area) requirement, depending on the frequency. For example, the ideal length of a quarter-wavelength antenna operating at 300 MHz is 25 cm. No matter how small the design of the circuit or chassis is, the size of the whole communication system is big due to the antenna.  
For the last decade, a vast amount of research has been conducted on the so-called electrically small antenna (ESA), which is defined by an antenna whose maximum dimension is less than \(\lambda/2\pi\)[1; 2]. Although an ESA presents a small footprint, it usually accompanies low radiation resistance and high reactance, which makes it difficult to match to the system impedance (e.g., 50 \(\Omega\)). To promote the impedance matching, often passive components, such as inductors (L) and capacitors (C), are used to remove the reactance at a designated frequency band. However, the matching bandwidth is extremely narrow, since the passive L, C, and the antenna itself follow the [PERSON]'s reactance theorem [3]. The latter asserts that the reactance must increase as the frequency increases.  
Figure 1a shows an example of adjusting the reactance of a capacitive ESA using an inductor. Both the C and L increase as the frequency increases, following [PERSON]'s reactance theorem. The ESA's capacitance is completely cancelled by the inductance at a single frequency, implying the matchingbandwidth is narrow. To overcome the bandwidth limitation of passive impedance matching, a non-Foster circuit (NFC) matching technique employing active components (e.g., transistor) has been introduced [4; 5]. The operation principle of an NFC is simple, as depicted in Figure 1b. It generates a negative C (or L), which is against the [PERSON]'s reactance theorem, and thus a broad reactance cancellation bandwidth can be achieved. Various non-Foster circuit designs have been reported for the broadband matching of small antennas [6; 7; 8; 9; 10; 11]. However, most of them presented only the enhancement in the antenna's reflection coefficient (S\({}_{11}\)) after applying the NFC, which is not sufficient to validate the system-wide improvement. It is important to examine the signal-to-noise ratio (SNR) since the active components employed in the NFC might introduce additional noise into the system [12; 13].  
In this paper, an NFC design with improved matching bandwidth and stability is presented. Compared to the previously designed NFC [6], this work has a much smaller footprint by shortening the microstrip line, and thus the overall loss and parasitic effect originating from the NFC can be reduced. More importantly, not only the impedance enhancement, but the received power and SNR enhancement after applying the NFC, is presented and discussed. The NFC was carefully designed, focusing on the reduction of internal loss, resulting in an average of 17.3 dB of received power improvement in the bandwidth of 150 to 300 MHz. To improve the stability of the NFC, a two-step validation check strategy of observing the stability condition in both frequency and time domains was applied. The NFC design is described in detail in Section 2. The noise power added by the implemented NFC was measured and the overall SNR enhancement was calculated. The results show that the proposed NFC provides an average of 7.3 dB of enhancement of SNR despite of the introduced noise. These measured results are discussed in Section 3.