Comparison of the advantages of network analyzers and sampling oscilloscopes TDR

Preface

In recent years, the bit rate of digital communication standards has been rapidly increasing with the popularity of multi-Gbps transmission. For example, the bit rate of USB 3.0 reaches 5 Gbps. The increase in bit rate has brought to light problems that have never been seen in traditional digital systems. Problems such as reflection and loss can cause digital signal distortion, resulting in bit errors. In addition, as the acceptable time margin for the correct operation of devices continues to decrease, the timing deviation problem on the signal path becomes very important. Radiated electromagnetic waves and coupling generated by stray capacitance can cause crosstalk, causing errors in device operation. As circuits become smaller and more compact, this problem becomes more and more obvious. Even worse, the reduction in power supply voltage will lead to a decrease in signal-to-noise ratio, making the operation of devices more susceptible to noise. Although these problems increase the difficulty of digital circuit design, the pressure on designers to shorten development time has not been reduced at all.

As bit rates increase, the above problems are unavoidable, but they can be detected and characterized using high-precision measurement instruments. The following are the measurement requirements that must be followed when using instruments to handle these problems:

A. A wide frequency range requires a large measurement dynamic range.
One way to achieve a high dynamic range is to reduce noise. If the instrument noise is minimized, very small signals (such as crosstalk signals) can be measured. It is also critical to accurately measure high-frequency components because they are the most common cause of signal integrity problems.

b. The excitation signal must be accurately synchronized.
When measuring the timing deviation of signals between multiple microstrip lines, accurately synchronized excitation signals can better ensure accurate measurement results.

c. Rapidly perform measurements and refresh the measurement results displayed on the instrument screen.
The ability to quickly perform measurements and refresh the displayed measurement results can make product design more efficient and improve production throughput.

Traditionally, time domain reflectometry (TDR) based on sampling oscilloscopes has been used for testing cables and printed circuit boards. Since such oscilloscopes have relatively large noise, it is difficult to achieve high dynamic range and fast measurement at the same time. Although the noise can be reduced by averaging, this will affect the measurement speed. The jitter between the multiple signal sources on the oscilloscope used to measure timing deviations can also cause measurement errors. In addition, it is very difficult to design electrostatic discharge (ESD) protection circuits for TDR oscilloscopes, so TDR oscilloscopes are easily damaged by ESD.

These problems are difficult to solve with a TDR oscilloscope alone and can only be solved with the E5071C-TDR, a TDR solution based on a vector network analyzer (VNA).

Time Domain Reflectometry Measurements Using a Vector Network Analyzer

What measurements does a VNA perform?
A VNA is an instrument that measures the frequency response of a device under test (DUT). During measurement, a sinusoidal excitation signal is input to the DUT. The measurement result is obtained by calculating the vector amplitude ratio between the input signal and the transmitted signal (S21) or reflected signal (S11) (Figure 2). The frequency response characteristics of the DUT can be obtained by scanning the input signal within the measurement frequency range (Figure 3). Using a bandpass filter in the measurement receiver can remove noise and unwanted signals from the measurement result, improving the measurement accuracy.

Figure 2. Schematic diagram of input signal, reflected signal, and transmitted signal.

Figure 3. The frequency response of a device under test can be measured using a VNA by sweeping a sine wave stimulus across the measurement frequency range.

Transform from frequency domain to time domain (inverse Fourier transform)

As we all know, the relationship between the frequency domain and the time domain can be described by Fourier theory. By performing an inverse Fourier transform on the reflection and transmission frequency response characteristics obtained using a VNA, the impulse response characteristics in the time domain can be obtained (Figure 4). Then, by integrating the impulse response characteristics, the step response characteristics can be obtained. This is the same response characteristic observed on a TDR oscilloscope. Since the integral calculation is very time-consuming, the method actually used is to perform calculations in the frequency domain based on the convolution principle of the Fourier transform—convolute the Fourier transform of the input signal and the frequency response characteristics of the device under test, and then perform an inverse Fourier transform on the result. Since the integral in the time domain can also be described using the convolution in the frequency domain, we can quickly calculate the step response characteristics.

Figure 4. Relationship between the step response and impulse response characteristics derived from the inverse Fourier transform.

The time resolution and time measurement range of the time domain characteristics obtained by inverse Fourier transform correspond to the inverse of the highest measurement frequency and the inverse of the frequency scanning interval, respectively (Figure 5). For example, if the highest measurement frequency is 10GHz, the time resolution is 100ps. We seem to think that the time range of measurement can be infinitely expanded by continuously reducing the frequency scanning interval, but in fact there is a limit. Because the frequency data used in the inverse Fourier transform must be equidistant in the frequency domain, if the frequency interval of the scan is smaller than the lowest measurement frequency of the VNA, then the inverse Fourier transform cannot be performed. For example, if the lowest measurement frequency of the VNA is 100kHz, the maximum time measurement range that can be obtained in the time domain measurement is 10 µs, which is sufficient for TDR measurement applications.

Figure 5. Relationship between time domain parameters (time resolution and time measurement range) and frequency domain parameters (maximum frequency and scanning frequency interval).

Figure 6 shows the correlation between the response curves obtained by measuring the impedance of the same DUT (with Hosiden’s test fixture and cables) using a VNA-based TDR (Agilent E5071C-TDR) and an oscilloscope TDR (Agilent DCA 86100C TDR). The difference between the two measurements is less than 0.4 Ω.

Figure 6. Correlation between the measurement results of the E5071C-TDR and the 86100C TDR oscilloscope (86100C) (the oscilloscope TDR measurement results are obtained after 16 averages).

Comparison of Dynamic Range between VNA and TDR Oscilloscopes

The previous document 1 has introduced the limitations and accuracy of VNA and TDR oscilloscopes. This section will compare the dynamic range of VNA and TDR oscilloscopes from a theoretical perspective. VNA and TDR oscilloscopes have different dynamic ranges due to their different architectures.

The following assumptions will simplify the comparison process:
● The noise and bandwidth (fc) of both systems are equal
● The noise is uniform (white) from DC to fc, and the observed power is b2
● The maximum signal power (a2) of the step input of the TDR oscilloscope and the sine wave input of the VNA oscilloscope are equal
● The transmission path between the signal source and the receiver is lossless
● Normalized impedance is used to simplify the numerical expression

The first thing to compare is the dynamic range of the same measurement. The time domain response of a TDR oscilloscope consists of a step stimulus and noise, with the power of each component defined as a2 and b2, respectively, and the dynamic range is the ratio of these components. For the VNA, the bandpass filter can transmit the signal losslessly, so the signal power is a2; the noise component is attenuated in the stop band of the bandpass filter—if the bandwidth of the bandpass filter is fIF, the noise attenuation at the filter output port is fIF/fC. Since the reduction in noise is proportional to the dynamic range, the measurement dynamic range of the VNA TDR can be expanded by 10 log(fC/fIF)dB. Since this relationship is independent of the stimulus frequency, the dynamic range of the time domain response obtained from the VNA measurement results after the inverse Fourier transform will also be expanded by 10log (fC/fIF)dB compared to the TDR oscilloscope.

Figure 7. Principle of VNA noise reduction.

Next, the comparison is made on the measurement time required to obtain the time domain response characteristics under the same time measurement range (T) and time resolution conditions.

When using a TDR oscilloscope to measure, in order to obtain the equivalent sampling time fE at the physical sampling frequency fP, the measurement needs to take fE/fP times longer to complete (as shown in Figure 7). When the measurement time length is T, it is necessary to measure T x fE data points (M), and the measurement time is T x fP/fS. When using a VNA to measure, if you want to obtain the same time domain response characteristics (as shown in Figure 9), you need to use 1/T as the frequency scan step and measure M*2 data points. The measurement time of a single data point is mainly determined by the bandpass filter, which is equal to 1/fIF. Therefore, the total measurement time is M x 1/fIF, which is equal to (Tx fE)x 1/fIF.

The comparison results show that the TDR oscilloscope can measure fP/fIF times in the time it takes the VNA to perform one measurement scan. Since averaging the signal waveform L times will cause the noise to decrease in direct proportion to fP/fIF, the TDR oscilloscope can expand the dynamic range by 10 log(fP/fIF)dB compared to the VNA.