Single Balanced Switching Mixer

A single balanced switching mixer is shown in Figure 1.


Figure 1. Single balanced switching mixer

MOS transistors M_1  and M_2 switch the current from the g_m-block between the + and – output terminals.  The differential LO signals that drive the switches   are shown in the Figure 1.

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

By Fourier series,

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

The output voltage v_o(t) of single ended switching mixer is given by,

(3)   \begin{eqnarray*} v_o(t) &=& v_{o2} - v_{o1} = -g_m R_L v_i(t)~[V_{LO^-}(t) - V_{LO^+}(t)]\\ &=& {4\over \pi} g_m R_L v_i(t) ~ \sum\limits_{n=1,3,5,...}^{\infty}{1\over n}\sin(n\omega_{LO}t)\\ &=& {4\over \pi} g_m R_L (V_b + V_{RF}\cos(\omega_{RF}t)) ~ \sum\limits_{n=1,3,5,...}^{\infty}{1\over n}\sin(n\omega_{LO}t)\\ &=& \begin{cases} {4\over \pi}g_m R_L V_{b}\underbrace{ \sum\limits_{n=1,3,5,...}^{\infty} \sin(n\omega_{LO}t)}_{\text{LO feedthrough}}\\ +{2\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*}

From Eq.(3), we can notice RF feedthrough suppression by differential LO signaling. Figure 2 illustrates the output voltage spectrum of a single balanced switching mixer.

Figure 2. Single balanced switching mixer output voltage spectrum

Figure 2. Single balanced switching mixer output voltage spectrum

Apart from sum and difference components due to mixing action, LO feedthrough still exists which is due to DC component in RF signal. This can be eliminated through differential RF signal in double balanced switching mixer.

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