# Design of a Fixed IF Down-Conversion Double-Balanced Mixer for UHF Band Applications
## 4 Simulation and Experimental Results
### Linearity  
The performance of most communication systems is limited by the mixer's dynamic range. The linearity of the mixer relies on the LO switches, the RF transconductance stages, and the tail current source. If the LO switches are ideal, the impedance observed when looking into the emitter of Q2 and Q3 is equivalent to that of the common base stage, i.e., \(\frac{1}{S=3}\). The voltage gain at the collector terminal of Q1 is extremely low, i.e., \(\frac{S_{\text{m1}}}{S=3}\), indicating that the \(1 IP_{3}\) of the mixer is determined by the RF transconductance stage Q1 rather than the LO switching core [27; 28; 29; 30].  
The linearization of the RF stage requires only the RF signal to be fed back while minimizing the LO and IF signals at the RF port is necessary to maintain port-to-port isolation. The collector currents of Q2, Q3, Q5, and Q6 are combined to ensure that the RF and LO signals cancel at the IF ports. The feedback applied only serves to linearize the RF stages and does not affect the mixing stages. Simultaneously, a shunt voltage feedback (Figure 17) is established between the collector of Q1 and the RF signal port node (\(V\_RF1\), \(V\_nRF1\)) through the resistor \(\RBT\).  
Figure 16: Single-sideband noise figure and conversion gain versus RF input frequency for fixed IF at 145 MHz.  
Figure 17: RF stage with feedback network.  
Figure 17 illustrates that inductive series feedback is located in the tail of transistors Q1 and Q4. The degenerative impedance of the first RF stage is determined by a 4.7 nH inductor (\(Z_{E1}\approx 21.983+j19.577\)), while a 2.2 nH inductor (\(Z_{E2}\approx 25.378+j12.609\)) was sufficient for linearization in the second stage. The current gain \(\beta\) varies by approximately 10 percent from one device to another. The variation in degenerative impedance in the two RF stages is much smaller compared to the \(\beta\) variation. The chosen inductor values are carefully designed and optimized to provide noise match.  
The input impedance \(Z_{in}\) of the dual feedback double-balanced mixer at RF is set by the feedback element R\({}_{B1}\) and degenerative impedance \(Z_{E}\):  
\[re\{Z_{in}\}\approx\ R_{B1}||(r_{b}+\frac{\beta}{g_{m}}+Z_{E}) \tag{33}\]  
The analysis is a large signal and is based on the Ebers-Moll equation. The derivation of the output current \(I_{F  
The graph in Figure 18 depicts the compression behavior of the down-conversion mixer relative to the RF input power. In this scenario, the frequency of the local oscillator is 855 MHz, the RF frequency is 1000 MHz, and the RF power increases in every simulation. The uncompressed gain measures approximately 11.4 dB, which is slightly lower than our initial estimate, and it decreases by 1 dB at \(-6.9\) dBm (approximately 143 mV). Accurately measuring the 145 MHz IF amplitude in the time domain is challenging due to the presence of LO feedthrough and signal distortion. Therefore, the analysis focuses on the fast Fourier transform (FFT) of the input and output [30; 31; 32; 33; 34; 35; 36].  
To evaluate the input IP3 of the mixer, we introduce two sinusoidal signals to the input, each with frequencies of 999.95 MHz and 1000.05 MHz. The peak amplitude of both signals is set at \(-30\) dBm. If the signal amplitude is too low, the \(1M_{3}\) components are affected by the FFT noise floor; if it is too high, the circuit may encounter higher-order nonlinearities. Figure 19 shows the mixer's down-converted spectrum, demonstrating a difference of \(\Delta P=P_{out}-P_{1M3}=73.214\) dB between the fundamental and \(1M_{3}\) tones. After this value is divided by two, and the input tone power is then added, we get \(1 IP_{3}=+6.716\) dBm in a 50-ohm system. A geometric interpretation of the above relationship is presented in Figure 20.  
Figure 19: Two-tone test of a 1 GHz down-conversion double-balanced mixer.  
Figure 18: Compression characteristics of the down-conversion double-balanced mixer.