## 3 Results and Discussion
### GFET Based Flexible Receiver
#### 3.5.2 Frequency Translation Block  
We describe in the following subsections two types of frequency translation blocks, GFET doublers and demodulators. GFET doubler is a frequency multiplier which can enable the realization of very high frequency communication circuits on soft substrates. On the other hand, a GFET demodulator described here does AM demodulation from carrier frequency to baseband. In general, graphene transistors can  
Figure 6: **(a)** Graphite Patch Antenna; **(b)** Measured and simulated response; **(c)** Simulated radiation pattern (adapted from [17], Copyright 2013, permission granted by [PERSON]). Figure 7: **(a)** Convex bending of graphite antenna; **(b)** Antenna is placed in the middle of test vice fixture; **(c)** Antenna response with convex bending of \(r=29\) mm (adapted from [17], Copyright 2013, permission granted by [PERSON]). also be modified to serve as a demodulator for a variety of communication schemes, such as amplitude shift keying (ASK), frequency shift keying (FSK) and phase shift keying (PSK) modulations [13]. (1) GFET Doubler  
We designed and fabricated a graphene doubler on flexible PI substrate. We will first discuss the operating principle of a GFET doubler. The input and output characteristics of an ideal square law transistor doubler are depicted in Figure 8.  
It has ambipolar input characteristics (even symmetry) due to current conduction by both holes and electrons. For positive gate bias (\(V_{\mathrm{GS}}>V_{\mathrm{dirac}}\)) electrons conduct and for negative gate bias (\(V_{\mathrm{GS}}<V_{\mathrm{dirac}}\)) holes conduct. Ideally, the Dirac voltage should be around 0 V. The drain current \(\mathrm{I_{DS}}\) is proportional to \(V_{\mathrm{GS}}\)[2]. On the other hand, the output current characteristic is linear (odd symmetry) with respect to the drain bias, \(V_{\mathrm{DS}}\). Using these two properties of an ideal square law device in our transistor model (Figure 2) we can derive an approximate expression for the output voltage:  
\[|v_{ds}|=\frac{g_{0}R_{L}\gamma V_{DS}v_{in}^{2}(\cos 2\omega_{in}t)}{2n_{0}+g_{ 0}R_{L}(2n_{0}+\gamma v_{in}^{2})} \tag{5}\]  
where \(\mathrm{g_{0}}\) and \(\gamma\) are scaling factors, and \(R_{L}\) is the load resistor. These parameters and coefficients are described in detail in our previous works [17, 22]. In Equation (5) we have neglected higher order terms in the simplified analysis. This working description clearly shows that GFET biased at Dirac point can be used as a frequency doubler [17]. In practice, there are several sources of non-idealities that can degrade doubler performance including charged impurities and contact resistance with consequent reduction of electron-hole symmetry and gate modulation. We fabricated a prototype GFET doubler biased at the Dirac point using the above concept. Figure 9a shows the schematic of the frequency doubler. A function generator is used to apply the RF input. Bias-Tees are used for input and output routing for DC bias, and an oscilloscope as the load to the doubler. Figure 9b shows the power spectrum. The conversion gain of our doubler is -29.5 dB [16]. This is relevant in the context of (flexible) RF transmitters which typically requires frequency upconversion. Figure 8: **(a)** Transfer and **(b)** Output Characteristics of an ideal square law transistor doubler (adapted from [22], Copyright 2011, AIP Publishing LLC). (2) GFET AM Demodulator  
In our goal towards the demonstration of a flexible graphene AM radio, we designed and fabricated a flexible GFET demodulator. The demodulator circuit is as shown in Figure 10a. The input is an AM modulated signal (2 KHz modulation frequency, 400 MHz carrier frequency). The output is connected to an oscilloscope through a low pass filter. Smoothening capacitors are used at the output to limit the spectra to the audio range. The GFET is biased close to the Dirac point. The ambipolar characteristic of GFET at the Dirac point (see Equation (5)) makes it to act as a square law AM demodulator.