## 4 Validation and Error Analysis of Extracting Transmission Characteristics
### Experiment Validation
#### 4.1.1 One-Trace Validation  
One-trace validation was performed with two kinds of printed traces, a corner trace and a via trace, as shown in Figure 7. Both PCBs had two layers and were produced from 1.6 mm thick FR4 substrate (\(\varepsilon_{r}=4.3\)) with dimensions of 90 mm \(\times\) 30 mm. The corner trace had a 0.5 mm wide trace and four 135 degree corners printed on the top layer, constructing a coplanar waveguide with the ground planes, and two through-hole SMA connectors were soldered at both ends of the printed trace. The width of the via trace was 0.5 mm, which was crossed at the center of the board by a 1.27 mm via, producing a coplanar waveguide with the ground planes. There are also two through-hole SMA connectors soldered at both ends of the printed trace, so that the signal can be injected into the trace.  
To verify the transfer function \(H_{T}(f)\), a 100 MHz trapezoidal waveform was injected to the tested printed trace, and the emission spectrum was measured at both ends of the trace. The distance between the tip of probe and the tested printed trace was 0.5 mm. The transmission coefficient was calculated by subtracting the amplitude of the emission spectrum tested at the load side from that which was tested at the input side in decibels. It was compared with the results obtained directly using a VNA. The amplitude of the original spectrum, the extracted harmonic amplitudes, and the corrected harmonic amplitudes of input signal and load signals are shown in Figure 8. Figure 9 shows that the transmission characteristics \(H_{L}(f)\) of a corner trace and a via trace obtained by two-sided measurement and VNA measurement are in good agreement up to 12 GHz. The mean variations of the two printed traces are 1.32 dB and 1.57 dB, respectively. The maximum errors are 5.6 dB at 11.3 GHz and 16.3 dB at 12 GHz, respectively, which shows that \(H_{T}(f)\) is effective.  
Figure 8: Amplitude of original, extracted, and corrected harmonics of the input and load signals.  
Figure 7: The one-trace validated structures. (**a**) Corner trace; (**b**) via trace.  
When only the load side was measured, a trapezoidal waveform of 100 MHz was injected to the tested printed trace. Figure 10 depicts the amplitudes of the predicted and measured input harmonics of the above two traces. The transmission characteristics \(H_{L}(f)\) acquired with the proposed method are compared with those measured using VNA in Figure 11. A wavelet packet [28] was applied to smooth the curves, as shown in Figure 12. After being processed, the transmission coefficients calculated with the proposed method agreed well with those obtained using a VNA below 12 GHz. The mean variation of the corner trace is 3.18 dB, and the maximum error is 6.7 dB at 11.3 GHz. The mean variation of the via trace is 3.52 dB, and maximum variation is 17.2 dB at 12 GHz. Except for 12 GHz, they can satisfy the requirements for engineering utilization.  
Figure 10: Amplitude of predicted and corrected harmonics of the input signal.  
Figure 9: The extracted transmission characteristics of a corner trace and a via trace measured at both ends compared with those obtained using a VNA.