# Ku-Band Mixers Based on Random-Oriented Carbon Nanotube Films
## 3 Results and Discussion
### Mixing Performance Characterization of Mixer  
Next, we further explore the conversion capability of RF devices based on randomly oriented CNT films. Based on the developed randomly oriented CNTs RF FETs, we built active mixers for frequency conversion. Our active mixers were measured according to the measurement schematic diagram shown in Figure 3a; the RF signal (\(f_{RF}\)) and the local oscillator signal (\(f_{LO}\)) were combined and applied to the gate terminal which modulated the device to realize the mixing function. Two bias Tees were used before the gate and drain terminals, respectively, to combine DC and RF signals while reducing the interference between DC bias and RF signals. The output signal of the mixer, also denoted as IF signals, was obtained from the drain terminal. When measuring the mixer for the first time, in addition to calibrating the test line, it was necessary to clarify the basic conditions of mixer measurement, including bias conditions, local oscillator power, and operating frequency band, as shown in Figure S3. Figure 3b shows the typical mixing result of a mixer with two adjacent frequencies as input signals of an RF (radio frequency) signal (\(f_{RF}\) = 10.1 GHz with power of \(-\)10 dBm) and an LO (local oscillator) signal (\(f_{LO}\) = 10 GHz with power of 7 dBm) combined into the gate. The output signal of the intermediate frequency signal (\(f_{IF}\)) was located right at 100 MHz, which was the frequency difference (\(f_{RF}-f_{LO}\) = 0.1 GHz). The typical conversion gain was about \(-\)11.4 dB, as shown in Figure 3c at 10 GHz of the X band. Figure 3: CNT-based active mixer: (**a**) measurement schematic diagram of the CNT-based active mixer; (**b**) the output spectrum of the CNT-based mixer at 10.1 GHz RF input signal with \(-\)10 dBm power and 10 GHz LO (local oscillator) signal with 7 dBm power; (**c**) the relationship between the RF signal power (\(P_{\text{RF}}\)) and the intermediate frequency (IF) signal power (\(P_{\text{IF}}\)) of the CNT-based active mixer at different operating frequencies from 10 GHz to 15 GHz; (**d**) 18 dBm IIP3 of the CNT-based active mixer operating at 10 GHz. According to [PERSON] et al. (2018), the conversion gain CG can be expressed by the transistor parameter as follows:  
\[CG=\frac{g_{m,max}^{2}R_{L}}{16\omega_{1}^{2}C_{S_{R}}^{2}R_{ll}} \tag{2}\]  
where \(g_{m,max}\) is the maximum transconductance, \(R_{\text{L}}\) is the load resistance of the IF signal port, \(\omega_{1}\) is the RF signal frequency, \(C_{\text{gs}}\) is the capacitance between the gate and the source, and \(R_{\text{il}}\) is the resistance of the input loop, including the intrinsic resistance of the gate, source, and field effect transistor. From Equation (2), the transconductance of the RF transistor is vital for mixers achieving maximum conversion gain, which would decrease as frequency increases. Figure 3c shows the relationship between the input RF signal power (\(P_{\text{RF}}\)) and output IF signal power (\(P_{\text{IF}}\)) at three different frequencies (\(f_{\text{RF}}\)) of 10 GHz, 12 GHz, and 15 GHz, covering from the X band to Ku band, while \(P_{\text{LO}}\) = 7 dBm. As the RF signal power scales up from \(-\)5 dBm to \(-\)0.5 dBm, the IF signal power correspondingly increases linearly without gain depression. The conversion gain is calculated by CG = \(P_{\text{IF}}-P_{\text{RF}}\), and it is \(-\)11.4 dB, \(-\)13.1 dB, and \(-\)17.5 dB, respectively, for three frequencies. Furthermore, linearity is also needed for mixers and other RF devices to keep RF signals undistorted. We demonstrated the CNT-based mixer's linearity by measurements shown in the Materials and Methods section. The 1 dB compression (P1 dB) point for CNT-based mixers is demonstrated as 4 dBm in Figure S4 of the Supplementary Materials. The third-order intercept point (IP3) is an important parameter to characterize the linearity of RF devices.