*3.2. Mixer Design*

The mixer is responsible for down-converting the RF signal to the IF signal using the LO signal. There are two well-known mixer architectures: the passive and the active mixer. The passive mixer is preferred over the active mixer due to its high linearity performance yielded by the current-mode operation. In the passive mixer, switches are biased in a linear region. The gate of the switches are biased to make sure that the LO signal is able to turn on the mixer switches when it toggles between 0 V and the supply voltage. The circuit diagram of the mixer is shown in Figure 4. The mixer input is ac-coupled using a capacitor to separate the LNTA biasing and block low-frequency noise. The drain and source of the mixer switches are biased by the TIA common-mode voltage.

**Figure 4.** Stacked receiver circuit diagram.

### *3.3. TIA Design*

The transimpedance amplifier (TIA) is used after the passive mixer to convert the IF current to an IF voltage at the output. In addition, it provides low-input impedance that improves the linearity. This work employs an inverter-based TIA using a feedback resistor to control the gain and a capacitor bank to define the IF bandwidth, shown in Figure 5. The current reuse inverter using both PMOS and NMOS enhances the overall transconductance without consuming extra power.

**Figure 5.** TIA circuit diagram.

The input impedance looking into the *INVn* input is given by

$$Z\_{\rm in} = \frac{R}{g\_m R\_{\rm out}} + \frac{1}{g\_m} \tag{6}$$

where *R* is the feedback resistor and *gm* is given by *gmp* + *gmn*.

The conversion-gain of the proposed receiver can be calculated as

$$CG \cong \frac{2}{\pi} \frac{\operatorname{Sim}(\pi d)}{2d} \mathbf{g}\_m \mathbf{R}\_{FB} \tag{7}$$

where d is the clock duty-cycle that is 12.5% in this work.
