The mixer is a critical component in wireless transceivers, significantly influencing the overall system performance. Two key parameters that define the quality of a mixer are linearity and conversion gain. In receiver systems, the mixer's conversion gain plays a vital role in reducing the complexity of subsequent stages, thereby improving noise performance and sensitivity. Linearity, on the other hand, determines the maximum input signal level the mixer can handle without distortion. As modern communication systems demand higher performance, both downconverters (mixers in receivers) and upconverters (mixers in transmitters) must achieve better linearity to meet these requirements. Therefore, designing a mixer with high gain and high linearity has become a major focus in the industry.
In CMOS circuit design, techniques such as current multiplexing and current injection are commonly used to enhance the linearity and conversion gain of mixers. However, current injection is limited in low-power applications due to the need for large injected currents to maintain good performance. In this paper, we present a high-gain and high-linearity mixer that utilizes current multiplexing along with the even harmonics of the local oscillator (LO) signal to improve performance.
**1 Circuit Design and Analysis**
**1.1 Circuit Structure**
In most receiver topologies, LO signals may leak due to coupling between the LO and RF paths through parasitic capacitance or the substrate. This leakage can occur in two main ways: first, the LO signal may appear at the intermediate frequency (IF) output, and second, it can enter the mixer directly via capacitive coupling or be amplified by the low-noise amplifier (LNA) before reaching the mixer. This results in DC offset interference in zero-IF systems and reduces the dynamic range of the IF signal. To mitigate these issues, an even harmonic mixer is employed.
The mixer designed in this paper uses the topology shown in Figure 2. This structure incorporates a local oscillator frequency multiplier and a current multiplexing circuit to enhance port isolation, conversion gain, and linearity. The differential LO input creates a virtual ground at node A, effectively shorting the LO signal and improving isolation. Additionally, when using short-channel transistors, the differential pair generates the LO multiplication signal at node A, which is analyzed later. The RF signal is then mixed with the second harmonic of the LO signal, resulting in an IF frequency of |fRF - 2fLO|. Using LO harmonics avoids LO leakage and reduces the LO frequency by half, simplifying the oscillator design. The inductor LE in the structure enhances the amplitude of the second harmonic entering the mixer, improving linearity and noise performance. It also acts as a push-pull enhancement, increasing the current and expanding the dynamic range of the multiplexed circuit. The IF output is connected to a source follower as an output buffer.
**1.2 Current Multiplexing Circuit Analysis**
The current multiplexing structure at the RF input consists of MRFP1, MRFN1, MRFP2, and MRFN2, as shown in Figure 2. This symmetrical structure increases the transconductance (gm) across the stage, contributing to higher gain. The transconductance is given by gm = gmp + gmn, where gmp and gmn are the transconductances of the PMOS and NMOS transistors, respectively. This configuration boosts the overall gain of the mixer.
From the channel length effect, the cross-coupled current expression is:
$$ I_{\text{cross}} = n \cdot (V_{\text{in}} - V_t)^2 $$
Where $ n $ is the transconductance parameter, $ V_{\text{in}} $ is the input signal, $ V_{\text{ov}} = V_{\text{GS}} - V_t $ is the overdrive voltage, and $ V_t $ is the threshold voltage. The output current can be derived from this equation, and it shows that the transconductance of the current multiplexing structure is the sum of the individual transistor transconductances.
When the input signal is positive, the MRFN transistors operate in saturation while MRFP transistors are in cutoff, acting like resistors. This makes the structure behave like an n-channel common-source amplifier. Conversely, when the input is negative, the structure functions as a p-channel common-source amplifier. This push-pull configuration expands the dynamic range and improves the linearity of the circuit.
**1.3 Frequency Multiplier Circuit**
To further analyze the LO signal multiplication, the inductive frequency multiplier circuit in the mixer is shown in Figure 3. The leakage currents from transistors MLON1 and MLON2 can be expressed as:
$$ I_{\text{LO+}} = n \cdot (V_{\text{LO}} - V_{\text{TN}})^2 $$
$$ I_{\text{LO-}} = n \cdot (V_{\text{LO}} - V_{\text{TN}})^2 $$
The total current flowing through the multiplexing and frequency multiplying circuits is the sum of these two components. This results in a second harmonic signal at node VCOM, while the fundamental frequency is canceled out. With an inductor impedance of $ Z_{\text{LE}} = R_{\text{LE}} + j2\omega_{\text{LO}} L_E $, the voltage at the mixing point $ V_a $ is:
$$ V_a = V_{\text{COM}} \cdot \frac{Z_{\text{LE}}}{R_{\text{LE}}} $$
This increases the amplitude of the second harmonic signal, enhancing the mixer’s performance and improving linearity and noise figure.
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