# Design of a Fixed IF Down-Conversion Double-Balanced Mixer for UHF Band Applications
## 3 Proposed Down-Conversion Mixer Design  
The proposed differential down-conversion double-balanced architecture is shown in Figure 2. It comprises four Infineon BFP640 devices functioning as switches for the LO feed and two BFP840 devices designated for differential RF input. The Infineon BFP840 device was selected for the RF stage due to its higher \(f_{T}\) frequency and lower internal base resistance. We need the higher LO drive for the local oscillator stage. The output 1 dB compression point for the BFP640 device is roughly +11 dBm, whereas for BFP840, it is about 5 dBm. The design is based on coupled differential amplifiers, enabling the Gilbert cell to achieve high gain, low noise, wide bandwidth, and low power consumption, making it suitable for monolithic IC implementation. Figure 2: Active differential double-balanced down-conversion mixer. This work presents the design and the optimization of a completely monolithic double-balanced down-conversion Gilbert-cell mixer with a single-ended RF input and an IF-tuned circuit with differential output at 145 MHz. The local oscillator frequency sweep ranges from 355 MHz to 1855 MHz and is applied differentially through a balun to the four local oscillator transistors. The mixer is designed for a frequency range of 500-2000 MHz, with the RF signal being fed differentially (single-ended to differential conversion) to the RF transistor, as seen in Figure 2. Each RF stage draws about 10 mA, and the supply voltage is 4 V. So, the total power consumption of the circuit is approximately 80 mW (Total power consumption = 2 \(\times\) 10 mA (each branch draws 10 mA) \(\times\) 4 V (supply voltage)). Each RF stage incorporates multiple feedback mechanisms to address the nonlinearity present in transistors. Simultaneously, the series feedback from the second stage to the first stage serves to correct the phase shift between the two RF currents and enhances the dynamic range of the mixer. The circuit employs dual feedback linearization at each RF stage, combining series inductive feedback (at the input side) and shunt resistive feedback (at the output side). Series feedback stabilizes input current, while shunt feedback controls output voltage, hence improving the nonlinear transfer characteristics of the transistor, reducing distortion, and ensuring a more linear performance of the circuit. The mixer circuit is less influenced by the source due to the high input impedance of the series feedback. It improves impedance matching at the input, reducing noise contribution at the RF stage, hence providing a high signal-to-noise ratio at the input. Shunt feedback limits noise propagation at the output as it decreases the output impedance, making it easier for the circuit to drive a load. This improves signal transfer to the next stage with minimal loss. The combined effect results in enhanced linearity, a wide dynamic range, and a low noise figure. A 1000 MHz RF frequency and a fixed IF frequency of 145 MHz are used in the design to achieve the best possible performance in terms of conversion gain, noise figure, linearity, and dynamic range. Two voltage-dependent current sources, each with the same bias current, are used in the double-balanced mixer. The IF-port current alternates between \(\mathrm{g_{m}V_{RF}}\) and \(-\mathrm{g_{m}V_{RF}}\), and the DC bias current \(\mathrm{l_{bias}}\) is always balanced as it passes through both loads. Thus, the differential output voltage \(\mathrm{V_{IF}}\) is independent of the biasing current. The IF-port current can be calculated as follows:  
\[I_{IF}=\ g_{m}V_{RF}\bigg{\{}\frac{2}{\pi}\mathrm{cos}(\omega_{RF}-\omega_{Lo} )+\frac{2}{\pi}\mathrm{cos}(\omega_{RF}+\omega_{Lo})+\frac{2}{3\pi}\mathrm{ cos}(\omega_{RF}-3\omega_{Lo})+\frac{2}{3\pi}\mathrm{cos}(\omega_{RF}+3 \omega_{Lo})+\cdots\bigg{\}} \tag{5}\]  
Therefore, the conversion gain of the Gilbert-cell mixer is as follows:  
\[GC=\frac{2}{\pi}g_{m}R_{L} \tag{6}\]  
Expression (6) shows that the gain of the double-balanced mixer is the same as that of a single-balanced mixer.