# Interference of Spread-Spectrum EMI and Digital Data Links under Narrowband Resonant Coupling
## 5 Impact of Spread Spectrum Modulations in a 4-QAM Channel under Resonant EMI Coupling
### Test Setup  
The interference generated by a synchronous buck DC-DC converter has been measured and added in simulation to the input signal of a 4-QAM digital communication channel under resonant coupling with \(Q=1\) and \(Q=100\). In order to extract the EMI waveforms, the test setup in Figure 9, which is the same presented in [35], is considered. Here, a DC-DC power converter is intentionally designed to interfere with a digital data link. The converter is a hard-switched synchronous Buck operated from an input voltage \(V_{\text{IN}}=16\) V and connected to a load \(R_{\text{L}}=10\)\(\Omega\) in open-loop mode with a fixed duty cycle \(D=0.375\). Such a converter is driven by a 100 kHz PWM signal generated by a microcontroller, which can programmed to operate at constant frequency or with an SS random frequency modulation with  
Figure 8: Worst case and average normalized capacity loss over different resonant frequencies \(f_{\text{R}}\) versus SS-modulation depth \(\delta\) ranging from 0 (no SS) to 25% for different values of the resonant coupling quality factor \(Q\) under constant coupling integral. different modulation depth \(\delta\). The EMI voltage \(v_{\rm c}\) at the receiver input without SS-modulation and with random SS-modulation at different modulation depth \(\delta\) is acquired by a digital scope at 125 MS/s during the DC-DC converter operation and is stored in a database. The power spectral density of the measured waveform for periodic and random SS-modulated (\(\delta=6\%\)) is reported in Figure 10.  
Then, the measured EMI waveforms are added in simulation to the input of a 4-QAM receiver, modelling the EMI propagation path to the receiver as a resonant transfer function \(G(f)\) with \(Q=1\) and \(Q=100\) to discuss the impact of different resonant coupling mechanisms. For this purpose, a 4-QAM communication scheme over an AWGN channel with \(B=600\) kHz bandwidth is considered and the effects of non-modulated and SS-modulated EMI coupled to the channel bandwidth with a resonant transfer function with \(Q=1\) and with \(Q=100\) have been simulated in the Matlab environment, adding the measured non-modulated and SS-modulated EMI waveforms generated by the power converter to the received input signal. In Figure 11, resonant coupling with \(Q=1\) is considered and the BER is plotted versus the r.m.s. EMI amplitude (disturbances with different amplitudes have been obtained applying a scaling factor  
Figure 10: Measured power spectral density of periodic and random SS-modulated (\(\delta=6\%\)) EMI. Figure 9: Schematic view of the test setup. to the same measured EMI waveforms) for different values of the modulation depth \(\delta\). From the figure, it can be observed that the EMI amplitude at which BER starts increasing in a significant way is lower for a larger SS-modulation depth and higher in the non-modulated case or for small values of \(\delta\). Comparing non-modulated EMI with SS-modulated EMI, a similar BER is achieved for a 20% higher EMI amplitude in the non-modulated case. In Figure 12, the same analysis is performed under resonant EMI coupling with quality factor \(Q=100\). In this case, a similar BER is achieved for a 3.4X higher EMI amplitude than in the non-modulated cases, revealing an even worse impact of SS-modulations on the BER when an EMI resonant coupling with a higher \(Q\) factor is introduced. Based on the same analysis described above, the BER has been plotted for different EMI power levels versus the modulation depth \(\delta\) in Figure 13 for \(Q=1\) and in Figure 14 for \(Q=100\) and also in this case a worse BER degradation with increased SS-modulation depth is observed for resonant coupling with an increased quality factor. Figure 11: Bit error rate of a communication channel corrupted by SS-modulated EMI under weakly resonant coupling (\(Q=1\)) vs. EMI normalized r.m.s. amplitude at different modulation depth \(\delta\).