# A Low Phase Noise Frequency Synthesizer with a Fourth-Order RLC Loop Filter
## 5 Experimental Results
### Phase Noise Test  
The instrumentation adopts the E4440A spectrometer from Keysight and the MSO64B oscilloscope from Tektronix. The passive fourth-order RC filter and the passive fourth-order RLC filter are chosen as the loop filter. The phase noise of a signal is evaluated with an output frequency of 1426 MHz.  
Figure 9 presents the output signal's frequency spectrum. The output signal power is 5.36 dBm, which is lower than the typical output value of 6 dBm due to some attenuations caused by the test cable and the instrument.  
The experimental phase noise is shown in Figure 10. Compared with the passive fourth-order RC filter, the passive fourth-order RLC filter has better phase noise proximal to the useful signal, and its surrounding noise is weaker. Therefore, the passive fourth-order RLC filter has a better filtering effect. The experimental results correspond to the theoretical derivation and simulation results. The output phase noise of the passive fourth-order RLC filter reaches \(-105.59\) dBc@1 KHz. Due to the superposition of external noise, such as circuit and instrumentation, the experimental result deviates from the simulation result (below 8 dB). In addition, there is a curve bump at the distal of the signal due to the high-pass noise from the chip's internal VCO.  
Figure 8: Loop capture time simulation results: (**a**) passive fourth-order RC filter and (**b**) passive fourth-order RLC filter.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Passive Fourth-Order RC** & **Passive Fourth-Order RLC** \\  & **Filter** & **Filter** \\ \hline loop capture time (us) & 29.2 & 30.1 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Loop capture time simulation results.  
The phase noise of the designed frequency synthesizer can reach \(-93.84\) dBc/Hz@1 KHz, \(-82.56\) dBc/Hz@1 KHz, \(87.27\) dBc/Hz@1 KHz, and \(-86.5\) dBc/Hz@1 KHz using an active second-order filter in [24], an active third-order filter in [25], a passive third-order filter in [11], and a third-order microstrip filter in [26], respectively. As shown in Table 6, and since the phase noise of the frequency synthesizer in this design is superior to the mentioned references, this design has low phase noise performance.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Loop Circuit Type**} & \multicolumn{4}{c}{**Phase Noise (dBc/Hz)**} \\ \cline{2-5}  & **1 KHz** & **10 KHz** & **100 KHz** & **1 MHz** \\ \hline passive fourth-order RC filter & \(-98.25\) & \(-103.49\) & \(-101.82\) & \(-138.59\) \\ passive fourth-order RLC filter & \(-105.59\) & \(-103.66\) & \(-104.84\) & \(-130.27\) \\ active second-order filter [24] & \(-93.84\) & \(-95.23\) & \(-92.07\) & \\ active third-order filter [25] & \(-82.56\) & \(-93.34\) & \(-99.77\) & \(-96.79\) \\ passive third-order filter [11] & \(-87.27\) & \(-90.27\) & \(-93.26\) & \(-112.97\) \\ third-order microstrip filter [26] & \(-86.5\) & \(-85\) & \(-87\) & \(-115\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of phase noises of different filters.  
Figure 10: Output signal phase noise: (**a**) passive fourth-order RC filter and (**b**) passive fourth-order RLC filter.  
Figure 9: The output signal’s frequency spectrum.