How to analyze PCB impedance and loss

The impedance and loss of PCB are very important for the transmission of high-speed signals. In order to analyze such a complex transmission channel, we can study its impact on the signal through the transmission channel impact response.

The impulse response of a chirped circuit can be obtained by transmitting a narrow pulse. The ideal narrow pulse should be a narrow pulse with infinitely narrow width and very high amplitude. When this narrow pulse is transmitted along the transmission line, the pulse will be stretched. The shape of the stretched pulse is related to the response of the line. Mathematically speaking, we can convolve the channel's impulse response with the input signal to get the waveform of the signal after transmission through the channel. The impulse response can also be obtained by the step response of the channel. Since the derivative of the step response is the impulse response, the two are equivalent.

It seems that we have found a solution to the problem, but in the real situation, ideally narrow pulses or infinitely steep step signals do not exist. It is not only difficult to generate but the accuracy is not easy to control, so more in actual testing The ground is obtained by using a sine wave to obtain the frequency domain response, and the corresponding physical layer test system software is used to obtain the time domain response. Compared to other signals, a sine wave is easier to generate, and its frequency and amplitude accuracy are easier to control. Vector network analyzer VNA (vector networkanalyzer) can accurately measure the reflection and transmission characteristics of the transmission channel to different frequencies in a frequency range of up to tens of GHz through a sine wave sweep. The dynamic range is more than 100dB. In the analysis of the transmission channel, a vector network analyzer is mainly used for measurement.

The reflection and transmission characteristics of the system under test for sine waves of different frequencies can be expressed by S-parameters. S parameters describe the transmission and reflection characteristics of the device under test for sine waves of different frequencies. If we can obtain the reflection and transmission characteristics of the transmission channel for sine waves of different frequencies, we can theoretically predict the effect of the real digital signal after passing through this transmission channel, because the real digital signal can be considered as being caused by Made up of many sine waves of different frequencies.

For a single-ended transmission line, it contains 4 S parameters: S11, S22, S21, S12. S11 and S22 respectively reflect the reflection characteristics of 1-port and 2-port sine waves of different frequencies, S21 reflects the transmission characteristics of sine waves of different frequencies from 1-port to 2-port, and S12 reflects the 2-port to 1-port Transmission characteristics of different frequency sine waves. For the differential transmission line, since there are 4 ports in total, the S parameters are more complicated, with a total of 16 ports. In general, a vector network analyzer with 4 or more ports is used to measure the differential transmission line to obtain its S parameter.

If the 16 S-parameters of the differential line under test are obtained, many important characteristics of this pair of differential lines have been obtained. For example, the SDD21 parameter reflects the insertion loss characteristics of the differential line, and the SDD11 parameter reflects its return loss characteristics.

We can further obtain more information by inverse FFT transforming these S parameters. For example, the time domain reflection waveform (TDR: Time Domain Reflection) is obtained by transforming the SDD11 parameters. The time domain reflection waveform can reflect the impedance change on the transmission line under test. We can also perform the inverse FFT transformation on the SDD21 result of the transmission line to obtain its impulse response, thereby predicting the waveform or eye diagram of digital signals with different data rates after passing through the pair of differential lines. This is very useful information for digital design engineers.

It can be seen that using a vector network analyzer (VNA) to measure the transmission channel of a digital signal, on the one hand, the RF microwave analysis method can be used to obtain very accurate transmission channel characteristics in the frequency range of tens of GHz; another On the one hand, by performing some simple time-domain transformations on the measurement results, we can analyze the impedance changes on the channel and the impact on the real signal transmission, thereby helping digital engineers to determine the backplane, cables, Connectors, PCBs, and so on, don't have to wait for the final signal to be rushed.