Designers and test engineers should carefully consider an application’s bandwidth requirements before selecting an instrument.
Engineers want accurate measurements over as broad a frequency range as possible. The commonly heard phrase is that measurements should extend from “DC to daylight.” With oscilloscopes offering 100 GHz or more, we are getting closer to that goal. However, several key factors matter when evaluating an instrument’s measurement bandwidth. This article provides some insight into bandwidth.
What is bandwidth?
Bandwidth measures the range of frequencies that an instrument, like an oscilloscope, can measure within a stated measurement accuracy. Bandwidth is measured in units of frequency, Hertz, and its multiples. Bandwidth thus governs the highest and lowest frequencies that an instrument can measure within a specified accuracy. Bandwidth is one aspect of an oscilloscope’s frequency response and is usually displayed as a Bode plot of measured amplitude and phase versus frequency.
When DC-coupled, oscilloscopes have a low-pass frequency response. The shape of that response varies by model. In general, low-cost instruments exhibit a single-pole response with a 6dB-per-octave roll-off. Mid-range to high-end oscilloscopes use what is called a “brick wall” response (Figure 1).
Figure 1 This graph compares an ideal single-pole and measured brick-wall frequency responses.
The single-pole response is the natural response of an analog front end, modeled as a resistor in series with a capacitor. It is a low-pass response that rolls off at -6 dB/octave above its -3 dB upper corner frequency. Its claim to fame is basically low cost.
The brick wall response is achieved using signal processing and has a very high roll-off rate. The intent is to have little signal loss up to the oscilloscope’s bandwidth and then have a high roll-off rate to suppress signals above the instrument’s Nyquist frequency to minimize aliasing. This gives the brick-wall response a wider usable bandwidth because it is flatter up to the instrument’s bandwidth.
Keep in mind that an instrument’s cost is proportional to its measurement bandwidth. Higher bandwidth generally requires specialized components and processing techniques.
Instrument settings that affect bandwidth
Most oscilloscopes offer a choice of input termination impedances; 50 Ohm and 1 Megaohm are common. The instrument’s bandwidth usually varies with the termination; 50 Ohm generally has the greater bandwidth.
The instrument’s input coupling also affects its bandwidth. An AC-coupled input, intended to suppress DC, will attenuate low-frequency signals below the lower cutoff frequency, usually about 10 Hz, producing an overall band-pass filter response.
Oscilloscopes also include analog band-limiting filters; typically, the filter bandwidths are 20 and 100 MHz, though this varies across models. Band-limiting filters help reduce noise in some applications.
How much bandwidth do you need?
Bandwidth requirements vary by application. Applications that primarily use sine waves require less bandwidth than those dealing with rectangular pulses. This is because the pulse waveform’s shape depends on multiple harmonics accompanying the signal’s fundamental frequency. For instance, a square wave is composed of a sine wave at the fundamental frequency and N odd harmonics, with the amplitude of the nth harmonic being the reciprocal of the harmonic number, N (Figure 2).
Figure 2 A square wave can be constructed by adding odd harmonics to the sine wave fundamental.
The greater the number of odd harmonics added to the fundamental, the closer the measured waveform approaches an ideal square wave. Current industry standards support having an instrument bandwidth wide enough to accept the fifth harmonic of a digital signal’s clock frequency. So, for a square wave with a fundamental frequency of “F” Hz, the suggested instrument bandwidth should be five times that value, or 5F.
Measurement bandwidth also affects the acquired signal’s rise time. In the single-pole case, the rise time, in seconds, is limited to 0.35 divided by the measurement bandwidth, in Hertz. The rise time of the brick-wall filter depends on the signal-processing algorithm used and varies by supplier and model. For the oscilloscope used in Figure 1, the rise-time limit is 0.45 divided by the bandwidth.
This information will guide the selection of an instrument’s bandwidth based on either harmonic content or required rise time.
Bandwidth and sampling rate
All sampled-data instruments must sample at more than twice the input bandwidth to prevent aliasing. Aliasing is a type of signal distortion in which high-frequency signal components above one-half the sampling rate (the Nyquist frequency) are folded back into the baseband spectrum of a signal (Figure 3).
Figure 3 These graphs compare correctly sampled and undersampled or aliased data acquisition.
A correctly sampled signal has a frequency-domain spectrum in which the baseband signal appears as upper and lower sidebands at multiples (images) of the sampling frequency. As the sampling rate decreases, the image frequencies also decrease and approach zero. If the sampling rate drops below a point where the lower sideband image falls within the instrument’s baseband analog bandwidth, it causes aliased signal distortion. So, keep the instrument’s bandwidth less than one-half the sampling frequency.
Currently available oscilloscopes with long acquisition memory lengths and high sampling rates are less likely to alias, but users should be aware of the possibility.
Can you have too much bandwidth?
In addition to aliasing due to instrument bandwidth, it is very possible to have more bandwidth than you need. Remember that all instruments generate noise and spurious signals. Manufacturers do their best to minimize noise, but it is still present. Much of the noise is spectrally flat broadband, or “white” noise, distributed across the instrument’s bandwidth. As you can imagine, the greater the measurement bandwidth, the greater the noise (Figure 4).
Figure 4 This graph shows the noise contribution to a measurement channel as a function of the channel bandwidth.
The figure shows time- and frequency-domain displays, along with rms noise-level measurements for a common 30 mV rms full-bandwidth noise input across four bandwidths. The top set of traces shows the noise input at the oscilloscope’s full 20 GHz bandwidth. The left-hand graph shows the time-domain trace. The right-hand grid displays the average Fast Fourier Transform (FFT) spectrum of the noise input. The noise spectrum is flat across the full 20 GHz bandwidth.
The lower sets of traces show time- and frequency-domain plots for bandwidths of 4.62 GHz, 1.16 GHz, and 0.32 GHz, respectively. The measurement parameters P1 through P4 measure the standard deviation of each channel’s amplitude. Standard deviation is also known as AC rms because it removes the mean value from the rms calculation, showing only the noise contribution, not the offset. P1 shows the mean rms level of the input noise as 29.7 mV. P2 reads the rms level of the noise band-limited to 4.62 GHz and has a value of 14.8 mV. P3 reads the rms level after filtering to 1.16 GHz as 7.2 mV. P4 reads the rms level for a bandwidth of 320MHz as 3.8 mV.
The peak-to-peak noise levels of the time-domain waveforms decrease as the bandwidth narrows, as seen in the time-domain views. The bandwidths step down by ratios close to 4:1, and the resulting rms levels decrease with bandwidth at approximately 2:1. So the noise level drops as the square root of the bandwidth.
Most mid- to high-range oscilloscopes have low-pass noise-reduction filters, like these, that can be applied to reduce the instrument’s bandwidth and improve the signal-to-noise ratio for signals that don’t require the oscilloscope’s full bandwidth.
Optional filtering applications may also be available, offering low-pass, high-pass, band-pass, and band-stop filters with programmable cutoff frequencies, attenuation, and flatness. These enable custom filter designs matched to the application, reducing noise and improving the signal-to-noise ratio.
Increasing an oscilloscope’s bandwidth
Newer technologies almost always require higher-bandwidth instruments. It is interesting to see how that bandwidth increase can be achieved. Three design techniques can extend a new instrument’s bandwidth. The first is using new, faster semiconductor devices. If you plot the highest bandwidth available in oscilloscopes from the three largest suppliers versus time, you will see that the increase in bandwidth due to improving semiconductor technology increases at an average rate of about 28 percent. This means bandwidth doubles about every 2.8 years.
Need improved bandwidth sooner than that? Signal processing can moderately increase bandwidth. Equalization is a signal-processing technique that measures an instrument’s frequency response and applies a frequency-dependent correction factor to flatten the channel. The limitation of equalization is basically the increase in noise when gain is used to compensate for attenuation. Signal processing can shape the instrument’s frequency response to improve characteristics such as spectral flatness.
The final approach to increasing bandwidth is to use RF heterodyning to combine multiple channels, each covering a different frequency band, and then combine them. For example, a four-channel oscilloscope with each channel having a 33 GHz bandwidth can be reconfigured to provide two channels, each with a 65 GHz bandwidth (Figure 5).
Figure 5 This block diagram is of a wideband oscilloscope using heterodyning to double the bandwidth of each channel. (Image source: Teledyne LeCroy)
One channel handles the baseband signal up to 33 GHz. The upper band from 33 to 65 GHz is down-converted and applied to the second channel. The two channels are then recombined at a higher sampling rate to produce a single channel spanning 0 to 65 GHz.
Conclusion
The maximum bandwidth of instruments, such as real-time oscilloscopes, ranges from DC to over 100 GHz. The cost of these instruments varies directly with the bandwidth. Designers and test engineers should carefully consider the application’s bandwidth requirements before selecting an instrument.
Arthur Pini is a technical support specialist and electrical engineer with over 50 years of experience in electronics test and measurement.
Related Content
- Oscilloscope rise time and noise explained
- Aliasing, the bane of sampled data systems
- Oscilloscope input coupling: Which should you use?
- Using oscilloscope filters for better measurements
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