*4.2. Active-Inductor and* 1/ *f Noise-Cancellation Design*

In [22], the mixer input is connected to the output node. This increases the RF signal loss, and it does not allow the circuit to maintain its performance at high RF. To overcome this, the proposed AI circuit isolates the mixer input from the output. The impedance looking into the AI circuit is low at DC, while it increases at RF. In this case, the signal loss is then limited to parasitic capacitors. MAI, CAI, and RAI form the AI circuit. The small Rs is used to boost the impedance at high frequencies with minimal impact at low frequencies. The impedance looking into the AI circuit is approximately given by

$$Z\_{AI}(\mathbf{s}) \stackrel{\sim}{=} \frac{\mathcal{g}\_{m,AI} R\_S (R\_{AI} \mathcal{C}\_{AI} \mathbf{s} + 1) + R\_{AI} \mathcal{C}\_{AI} \mathbf{s}}{\mathcal{g}\_{m,AI} R\_S \mathcal{C}\_{AI} \mathbf{s} + \mathcal{g}\_{m,AI} + \mathcal{C}\_{AI} \mathbf{s}} || \frac{1}{\mathbf{s} \mathcal{C}\_{par}},\tag{9}$$

where Cpar is the parasitic capacitance at the mixer input.

The stacked receiver front-end suffers from high low-frequency noise due to the direct coupling of the noise through the AI circuit. To overcome this issue, a 1/ *f* NC circuit is formed by the MNC transistors. It provides the signal path to the output with the opposite polarity to cancel the low-frequency noise and push the 1/ *f* corner to a lower frequency. The functionality of the 1/ *f* NC circuit is being verified in Figure 10. It shows the 1/ *f* noise corner is pushed to a very low IF when the 1/ *f* NC circuit is enabled, while the thermal noise remains almost constant.
