# High-Resolution Digital Oscilloscopes – Architecture and Tradeoffs

05 July 2013

### Several oscilloscopes available today offer more than 8 bits of vertical resolution. Oscilloscopes with up to 12 bits of vertical resolution are available from multiple manufacturers, with some claiming up to 15 bits of resolution.

In some cases, extra resolution is achieved by applying Digital Signal Processing (DSP) to the output of a standard 8-bit Analogue-to-Digital Convertor (ADC). In other cases, the extra resolution is achieved by using a 12-bit ADC. Some oscilloscopes use a combination of a 12-bit ADC and DSP to achieve more than 12bits of vertical resolution.

For several years, oscilloscopes have offered a high-resolution acquisition mode. Oscilloscopes specifically designed for and dedicated to making enhanced vertical resolution measurements are commonly referred to as “high resolution”, or “high definition” oscilloscopes.

What does “number-of-bits” mean?

Beware that there is no standard for specifying the enhanced number of bits for high-resolution digital oscilloscopes. This can be confusing when trying to compare specifications between competing brands.

All manufacturers specify the number of ADC bits and that number ranges from 8 to 12 bits. The number of unique digital codes or quantisation levels (Q levels) is 2n,where n is the number of ADC bits. An 8-bit ADC has 256 Q levels, whereas, a 12-bit ADC has 4096 Q levels. Provided there is a sufficient signal-to-noise ratio (SNR), more ADC bits allow finer details of the signal to be seen.

The term, “bits of resolution”, is sometimes used to specify the number of bits. Oscilloscope families that use this term typically use an 8-bit ADC and DSP to achieve greater than 8 bits of resolution. The most common DSP method used to increase the number of bits is an N-tap boxcar-averaging filter. Averaging by 2 adds one bit of resolution. A general expression for the number of bits of resolution, r, is shown in Equation 1.

Equation 1: r = n +log2(N) bits of resolution

For example, 12 bits of resolution is achieved with a 16-tap boxcar-averaging filter running on data from an 8-bit ADC.

Some manufacturers prefer to specify the “number of enhanced bits”. An enhanced bit is equivalent to an ideal ADC bit in terms of SNR. An implementation that provides m enhanced bits provides the same ideal SNR achieved by an ideal m-bit ADC. By using a boxcar-averaging filter on the output of an n-bit ADC, the number of enhanced bits, m, is given by Equation 2.

Equation 2: m = n + log4(N) enhanced bits

For example, a 64-tap boxcar-averaging filter running on data from an 8-bit ADC has 12 enhanced bits of resolution.

Another specification commonly used is “Effective Number of Bits” (ENOB). ENOB is a measure of the SNR for a digitised signal. The definition for SNR in dB is given by Equations 3. Another definition in terms of root-mean-square voltage (VRMS) is given by Equation 4. This definition is useful when computing the SNR for an oscilloscope. Equation 5 shows the relationship between ENOB and SNR.

Equation 3:SNRdB = 10 log10(Signal Power / Noise Power)

Equation 4: SNRdB = 20 log10(Signal VRMS / Noise VRMS)

Equation 5:ENOB = (SNRdB– 1.761)/ 6.02

Each additional effective bit improves the SNR by 6.02dB. An ideal 8-bit ADC has an ENOB of 8 and a SNR of 50dB. The noise from an ideal ADC is all due to quantisation effects. Ideal ADCs with more bits have lower quantisation noise and better ENOB. ENOB varies with frequency, and is generally specified for a particular frequency.

ENOB is a good figure of merit when comparing oscilloscope technologies. The ENOB is reduced by all of the noise and error sources in the oscilloscope including ADC quantisation noise, ADC differential nonlinearity, ADC integral nonlinearity, thermal noise, shot noise, and input amplifier distortion. Beware that the ENOB specification is usually much lower than the number-of-bits specification due to these noise and error sources. For example, an ENOB between 8 and 9 bits at high frequency, or equivalently, a SNR between 50dB and 56dB, is typical for a 12-bit high-resolution digital oscilloscope.

High-resolution waveform

Figure 1 shows three waveforms captured on a digital oscilloscope that supports the high-resolution acquisition mode. The input signal is a stair-step ramp signal generated by driving a DAC with a digital counter. The upper grid displays three waveforms with standard magnification. The lower grid displays all three waveforms overlaid with 10x magnification to show more vertical detail. The top waveform was captured at 2.5GSa/s with the high-resolution acquisition mode turned off. Notice all of the noise on the signal and the lack of detail. This is especially apparent in the 10x magnified view. In this case, quantisation is not noticeable because vertical dither has been added to the waveform to enhance the display. The middle waveform was captured at 2.5GSa/s with the high-resolution acquisition mode turned on and set to provide 12 bits of resolution. The bandwidth for this case is 554MHz. The noise is reduced significantly and more vertical detail can be seen. The bottom waveform was captured with more than 12 bits of resolution. This was achieved by setting the sample rate to 125MSa/s, which increased the vertical resolution to more than 12 bits and reduced the bandwidth to 28MHz. For this particular signal, 28MHz is sufficient bandwidth and provides the best SNR with the most vertical detail.

The signal traces shown in Figure 1 were generated on an oscilloscope that uses an 8-bit ADC and boxcar-averaging to implement the high-resolution acquisition mode. Equation 6 shows the approximate bandwidth for a boxcar-averaging filter.

Equation 6:Boxcar Bandwidth˜0.4428 Fs/N

For the middle trace in Figure 1, the bandwidth can be calculated as follows. The sample rate, Fs, into the boxcar averaging filter is 20GSa/s and the number of bits of resolution is 12 bits. Using Equation 1, the number of taps is 2(12 – 8) or 16 taps. The bandwidth is 0.4428 x 20G/16 or 554MHz. Most high-resolution oscilloscopes calculate and display the bandwidth automatically.

High-resolution acquisition

Figure 2 shows an architecture that is commonly used to implement a high-resolution acquisition system. A bandwidth limit filter runs on the analogue input signal to eliminate signal content above the Nyquist frequency. The Nyquist frequency is defined as half of the sampling frequency, Fs. Any signal content above the Nyquist frequency folds back into the passband causing undesirable aliasing.

The minimum sampling frequency required to prevent aliasing is twice the bandwidth of the band limited analogue signal. Aliasing is an issue for standard full-bandwidth oscilloscopes running at reduced sample rates. The corner frequency for the bandwidth limit filter is set to a value slightly larger than the maximum specified bandwidth, and is typically not reconfigurable to support lower sample rates. In a high-resolution architecture, aliasing is reduced significantly by running an N-tap low-pass FIR filter prior to down sampling. This filter attenuates signal content which would otherwise fold back into the pass band after down sampling.

Aliasing is less of a concern for a dedicated high-resolution oscilloscope because the corner frequency of the bandwidth limit filter is set based on the reduced maximum bandwidth specification. For example, a 4GHz oscilloscope running the high-resolution mode to achieve 12 bits of resolution at 500MHz must still set the corner frequency above 4GHz to support the maximum bandwidth available. A dedicated 500 MHz high-resolution oscilloscope, on the other hand, can set the corner frequency slightly above 500MHz, eliminating aliasing altogether.

The ADC shown in Figure 2 is an 8-bit ADC, but the architecture works equally well with higher-bit ADCs. Following the ADC is an N-tap filter and down sampler. The N-tap filter stage is not necessary in oscilloscopes that use a high-resolution ADC to achieve the enhanced number-of-bits specification. However, this stage is often still included to achieve even greater resolution beyond that of the ADC. Filters with uniform tap weighting are called boxcar-averaging filters. Boxcar-averaging filters are easy to implement and support very high input sample rates and a large number of taps.

However, the rectangular time response of the boxcar filter produces a Sin(x)/x response in the frequency domain (see Figure 3). The side lobes in the stop band region allow some signal content beyond the bandwidth to fold back into the pass band, resulting in additional noise, aliasing and distortion. To counter this, some oscilloscopes use non-uniform weighting of the taps to produce a more desirable frequency response. One such implementation is named “Enhance Resolution” or ERES. The filter taps are designed to produce a Guassian response which has no side lobes in the frequency domain and which eliminates undershoot, overshoot and ringing in the time domain.

The down sampler following the FIR filter is required to conserve acquisition memory to support long time ranges. In most implementations, the N-tap filter and down sampler are integrated into one block that only outputs one out every N samples. One artifact of down sampling is that it creates multiple images of the frequency response centered at integer multiples of the decimated frequency, Fs/N. The Nyquist frequency is reduced to Fs/(2N). Any signal content in the stop band region of the FIR filter, beyond Fs/(2N), folds back into the pass-band region causing additional noise, aliasing and distortion. To counter this, some oscilloscopes also implement an M-tap FIR filter on the output side of acquisition memory. The filtering to achieve high resolution averaging is shared between the M-tap and N-tap filters allowing the N-tap filter to be shorter and the sample rate for a given bandwidth to be higher.

Some high-resolution implementations store 16-bit samples into acquisition memory. For standard oscilloscopes which normally store 8-bit samples into memory, enabling the high-resolution mode divides the maximum memory depth in half.

Vertical dither is sometimes added to the signal to make a more pleasing display. Vertical dither fills the unused least significant bits (LSB’s) of the 16-bit samples with random noise. Each additional dither bit doubles the number of Q levels in the signal.

The optional M-tap FIR filter on the output side of acquisition memory is sometimes used to implement a digital bandwidth limit filter. Data throughput out of acquisition memory is typically much slower than into acquisition memory, making longer and higher fidelity DSP filters feasible to implement. Although this filter works well to eliminate noise and improve resolution on full-sample-rate data, it is susceptible to aliasing at reduced sample rates, because it runs after the down sampler. For that reason, the high-resolution filter architecture is generally preferred for reduced-sample-rate measurements.

Using Acquisition Averaging to Improve Vertical Resolution

Most digital oscilloscopes provide acquisition averaging as a way to reduce the noise and improve the vertical resolution. Unlike the high-resolution architecture, acquisition averaging does not reduce the bandwidth. However, it only works with periodic signals. Multiple traces of the signal, one for each trigger event, are averaged together. Each sample in the waveform is averaged with the same sample in the previous waveforms.

Some oscilloscopes allow acquisition averaging and high-resolution acquisition to run simultaneously, allowing the user to make tradeoffs between bandwidth and throughput.

Figure 4 shows a PRBS signal captured with a high-resolution oscilloscope set for 10 bits of resolution and 2GHz of bandwidth. It also shows the PRBS captured with acquisition averaging (4 averages) enabled. In this case, acquisition averaging produces a meaningless display because the PRBS signal is not periodic over the captured time range.

Why buy a high-resolution oscilloscope?

If the measurement application requires higher vertical resolution and moderate bandwidth, a dedicated high-resolution oscilloscope is probably the best choice. High-resolution oscilloscopes use the latest ADC and DSP technologies to provide superior resolution and noise performance. Aliasing is better controlled. No special mode or setup is required to achieve the higher resolution. Also, the number of bits and bandwidth are usually displayed. This makes the oscilloscope easier to use. However, the maximum bandwidth available for a high-resolution oscilloscope is typically less than is available for an 8-bit oscilloscope with equivalent pricing.

Figure 1: High-Resolution Signal Trace Examples

Figure 2: High-Resolution Acquisition Architecture

Figure 3: Impulse and Frequency Response for a 16-Tap Boxcar-Averaging Filter

Figure 4: HighResolution versus Acquisition Averaging For a PRBS Signal