# 光学和电磁学 Optics and Electromagnetism PHYS2007

previously presented for phase noise case except that the interference is downconverted by spurious signal, which is considered as a single tone. With the SNR of the baseband signal being,
$$S N R=\left(P_{S i g}+P_{L O}\right)-\left(P_{I n t}+P_{S_{p}}\right)>S N R_{\min }$$
After rearrangement,
$$P_{S p}-P_{L O}<P_{S i g}-P_{I n t}-S N R_{\min }$$
where $P_{S_{p}}-P_{L O}$ denotes the power of spurious signal in $\mathrm{dBc}$, relative to the carrier power. For example, Bluetooth standard specifies an interferer of $+30 \mathrm{~dB}$ at $2 \mathrm{MHz}$ away from the desired signal. The reference spur can be also at $2 \mathrm{MHz}$ away from the carrier if the frequency of the reference signal is $2 \mathrm{MHz}$. The minimum SNR requirement is $18 \mathrm{~dB}$, same as the previous example. Substituting the numbers, the spurious signal requirement results in $-48 \mathrm{dBc}$ at $2 \mathrm{MHz}$ from carrier.

## PHYS2007 COURSE NOTES ：

The stability factor for an amplifier is given as:
$$K=\frac{1+|\Delta|^{2}-\left|S_{11}\right|^{2}-\left|S_{22}\right|^{2}}{2\left|S_{21}\right|\left|S_{12}\right|}$$
where
$$|\Delta|=\left|S_{11} S_{22}-S_{12} S_{21}\right|$$
For unconditional stability, $K>1$ and $\Delta<1$. Thus, higher reverse isolation $\left(S_{l 2}\right)$ improves the stability of an amplifier. In a common-gate LNA, since the gate of the MOSFET is conventionally connected to an AC ground, there is no Miller effect associated with the feed-forward capacitor $C_{g d}$. This improves the reverse isolation and hence, the stability.