- 2.1 The Time Domain
- 2.2 Sine Waves in the Frequency Domain
- 2.3 Shorter Time to a Solution in the Frequency Domain
- 2.4 Sine Wave Features
- 2.5 The Fourier Transform
- 2.6 The Spectrum of a Repetitive Signal
- 2.7 The Spectrum of an Ideal Square Wave
- 2.8 From the Frequency Domain to the Time Domain
- 2.9 Effect of Bandwidth on Rise Time
- 2.10 Bandwidth and Rise Time
- 2.11 What Does Significant Mean?
- 2.12 Bandwidth of Real Signals
- 2.13 Bandwidth and Clock Frequency
- 2.14 Bandwidth of a Measurement
- 2.15 Bandwidth of a Model
- 2.16 Bandwidth of an Interconnect
- 2.17 The Bottom Line

## 2.14 Bandwidth of a Measurement

So far, we have been using the term *bandwidth* to refer to signals, or clock waveforms. We have said that the bandwidth is the highest significant sine-wave-frequency component in the waveform's spectrum. And, for signals, we said *significant* was based on comparing the amplitude of the signal's harmonic to the amplitude of an equivalent repeat frequency ideal square wave's.

We also use this term *bandwidth* to refer to other quantities. In particular, it can relate to the bandwidth of a measurement, the bandwidth of a model, and the bandwidth of an interconnect. In each case, it refers to the highest sine-wave-frequency component that is significant, but the definition of significant varies per application.

The bandwidth of a measurement is the highest sine-wave-frequency component that has significant accuracy. When the measurement is done in the frequency domain, using an impedance analyzer or a network analyzer, the bandwidth of the measurement is very easy to determine. It is simply the highest sine-wave frequency in the measurement.

The measured impedance of a decoupling capacitor, from 1 MHz up to 1 GHz, shows that below about 10 MHz, the impedance behaves like an ideal capacitor, but above 10 MHz, it looks like an ideal inductor. Such a measurement is shown in Figure 2-15. There is good, accurate data up to the full range of the network analyzer, in this case, up to 1 GHz. The bandwidth of the measurement is 1 GHz in this example. The measurement bandwidth is not the same as the useful application bandwidth of the device.

Figure 2-15 Measured impedance of a small 1206 ceramic decoupling capacitor. The measurement bandwidth for this data is 1 GHz.

When the measuring instrument works in the time domain, such as a time-domain reflectometer (TDR), the bandwidth of the measurement can be found by the rise time of the fastest signal that can be launched into the DUT. After all, this is a rough measure of when the higher-frequency components are small.

In a typical TDR, a fast step edge is created and its change due to interaction with the DUT is measured. A typical rise time entering the DUT is 35 psec to 70 psec, depending on the probes and cables used. Figure 2-16 shows the measured rise time of a TDR as about 52 psec. The bandwidth of the edge is 0.35/52 psec = 0.007 THz or 7 GHz. This is the bandwidth of the signal coming out of the TDR and is a good first order measure of the bandwidth of the measurement.

Figure 2-16 Measured TDR profile from the output of a 1-meter cable and microprobe tip, open at the end. The TDR rise time after the cable and probe is about 52 psec. The bandwidth of the measurement is about 0.35/52 psec = 7 GHz. The measurement was recorded with TDA Systems IConnect software, using a GigaTest Labs Probe Station.

In state of the art TDRs, calibration techniques allow the bandwidth of the measurement to exceed the bandwidth of the signal. The bandwidth of the measurement is set by when the signal-to-noise ratio of a frequency component is below a reasonable value, like 10. The bandwidth of the measurement of some TDRs can exceed the signal's bandwidth by a factor of 3-5, making the bandwidth of a TDR's measurement as high as 30 GHz.