Single Ended Switching Mixer


A single ended switching mixer is shown in Figure 1.

single-ended-switching-mixer

Figure 1. Schematic of a single ended switching mixer

The Linear g_m-block convert the RF signal from voltage to current domain.
The switch(S) is turned ON and OFF by the LO signal. LO signal is a square wave with 50% duty-cycle.

(1)   \begin{eqnarray*} V_{LO}(t) = \begin{cases} 1, & 0 < t < {T/2}\\ 0, & T/2 < t < T \end{cases} \end{eqnarray*}

By Fourier series,

(2)   \begin{equation*} V_{LO}(t) = {1 \over 2} + {2\over\pi} \sum\limits_{n=1,3,5,...}^{\infty} \sin(n\omega_{LO}t) \end{equation*}

When the switch is driven by LO, the RF signal gets multiplied by square wave … changes sign.

Therefore output voltage (v_o(t)) is given by,

(3)   \begin{eqnarray*} v_o(t) &=& V_{DD} - g_m R_L v_i(t) V_{LO}(t) \\ &=& V_{DD} - g_m R_L (V_{b} + V_{RF} \cos\omega_{RF}t) \left( {1 \over 2} + {2\over\pi} \sum\limits_{n=1,3,5,...}^{\infty} \sin(n\omega_{LO}t) \right) \\ &=& \begin{cases} \underbrace{V_{DD} - {1\over 2}g_m R_L V_{b}}_{\text{DC component}} \\ - {1\over 2}g_m R_L \underbrace{V_{RF} \cos\omega_{RF}t}_{\text{RF feedthrough}} \\ - {2\over \pi}g_m R_L V_{b}\underbrace{ \sum\limits_{n=1,3,5,...}^{\infty} \sin(n\omega_{LO}t)}_{\text{LO feedthrough}}\\ -{1\over \pi}g_m R_L V_{RF}\underbrace{\begin{cases}\left(&[\sin(\omega_{LO}-\omega_{RF})t+\sin(\omega_{LO}+\omega_{RF})t] \\ & + {1\over 3}[\sin(3\omega_{LO}-\omega_{RF})t+\sin(3\omega_{LO}+\omega_{RF})t]+\ldots \right) \end{cases}}_{\text{mixed components}} \end{cases} \end{eqnarray*}

Eq.(3) points out that, the output of a single ended mixer contain DC, RF feed-through, LO feed-through and mixed components.
RF feedthough to the output is due to DC component in LO signal.
LO feedthrough is due to DC component in the RF signal.

se-switching-mixer-freq-spectrum

Figure 2. Output voltage spectrum of single ended switching mixer

Figure 2. illustrates the output voltage spectrum of a single ended switching mixer. The LO feedthrough problem of single ended mixer can be mitigated  through single balanced switching mixer using  differential LO signals.

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