You use this digital filter knowingly or not, every day – it is inherently built into every Digital Volt Meter (DVM) by the fact that a common DVM is set to integrate its input signal over one line frequency cycle on every measurement. Most people know that the integration period of 1/60 Hz (or 1/50 Hz depending on where you live), or one power line cycle, allows the DVM to reject the 50 or 60 Hz noise and that noise is everywhere. You simply can’t get away from line frequency voltages and interference in the modern world. It turns out that this natural line frequency rejection is a form of a digital filter and it follows the Sine X / X, or Sinc() function as shown in Figure 1.
Figure 1 – Sine X / X, or Sinc() function frequency response. This response is ‘naturally’ built into every DVM by their integration over an exact number of power line cycles. This sampling then provides a null at the power line frequency, providing rejection to any power line noise. This is perhaps the most common form of a Digital Filter Around. The Blue Curve above is the Sync() filter frequency response, the Orange lines are the asymptotes that converge on the -3 dB response point.
The Sync() function is equivalent to sampling the input voltage with a rectangular window of time T.
The great advantage of the Sync() function is a Null at known intervals, and smooth transient response, this is of great advantage in a DMM. Its disadvantage is the passband is not very flat and has a long, droopy roll-off as is characteristic in these linear phase sort of filters.
As figure 1 shows the -3dB point is at 0.45 times the first null frequency. Table 1 lists some other pertinent roll-off points. The Frequency is normalized to the first null frequency.
Table 1 – A Sync() filter has various amplitude roll-off points as listed in the table above. The frequency is normalized to the first null frequency. Example: A DMM integrating for 1/60 seconds would have a -6 dB noise bandwidth at 36 Hz (60Hz*0.61 = 36Hz).
This same filter function happens if I take a 1 Mega-Sample Per Second (MSPS) ADC and store it, then average the samples over a 1/60 Hz (16.6 milli-second) period. Essentially the ‘integration time’ is 1/60 Hz and the same Sinc() filter function is again the result.
The integration time of the DVM can also be thought of as the ADC’s ‘Aperture Time’. That 1 MSPS ADC that was used in the averaging example also has an ‘Aperture Time’ that is the length of time that its internal Sample and Hold takes to switch from: Acquire to Hold modes. Aperture time, as the Analog Devices tutorial on Sample and Hold Amplifiers [1] points out,
“Perhaps the most misunderstood and misused specifications are those that include the word aperture. The most essential dynamic property of an is its ability to disconnect quickly the hold capacitor from the input buffer amplifier. The short (but non-zero) interval required for this action is called aperture time.”
Yes, misunderstood and in modern ADC’s not even commonly specified on the datasheet! The Acquisition Time is commonly specified as the time required to acquire any signal to the specified accuracy, but the Aperture Time itself is not.
Most higher speed ADC’s now have a very, very, very small Aperture Time, this can be inferred by the Analog input bandwidth which is usually much, much greater than the ADC's Nyquist frequency. For instance: A Linear Technology LTC2328-16, 16 Bit, 1 MSPS ADC has a specified analog input bandwidth of 7 MHz. The Data Converters have these large bandwidths to accommodate under-sampling and Nyquist folding of the input signals. In the LTC2328 case, this input bandwidth limitation is due to the Analog Input Circuit inside the ADC, not the Aperture Time. As an example calculation on the upper limit of Aperture Time on this ADC let's assume that the input bandwidth is set by the Aperature time and not the RC time constants in the ADC’s input circuit.
From Table 1 the -3dB point is found to be 0.45 the first null frequency, so if the -3dB point is 7 MHz, that would mean that the Aperture Time of this ADC is: 7 / 0.45 = 15 MHz or 1/15 MHz = 66 nSec. This is entirely wrong of course as the input bandwidth is not set by the Aperture Time, but by the input circuits time constants. This is however an upper limit on how big the aperture time could be to explain the input bandwidth effect, meaning: “The Aperture Time could not be longer than this and still get the rated input bandwidth of 7 MHz”
Analog Bonus Circuit
It is possible to simulate the Sync() filter with an OPAMP active filter circuit. Philbrick / Nexus research published this analog Sync() filter way back in 1968 and was named after its inventor, Henry Paynter who was a partner in the firm [2].
This circuit of figure 2 is a Third Order Liner Phase Shift ‘Paynter’ filter. Paynter filters are still widely used today in filtering biological types of signals and are even synthesized in many ‘digital’ implementations.
As per Philbrick: “...This filter is particularly useful for averaging functions of non-stationary random variables since its transient-response time is minimum for a given averaging time…” [3]
Figure 2 – The circuit for a Paynter filter that simulates a Sync() function response. All the values are normalized to the ‘notch frequency’.
Notch is at Wc = 1/(RC) or Fc = 1/(2*PI*R*C) Hz
Figure 3 – Frequency Response of the Paynter filter of figure 2 (Orange Curve) with the ideal Sync() filter response superimposed on it (Blue Curve). This filter was designed to have the 'Null' at 60 Hz.
Figure 4 – Linear phase filters like the Paynter have good transient response without excessive overshoot as shown from this LTSpice simulation of figure 2.
References:
[1] Analog Devices “Sample-and-Hold Amplifiers” MT-090
[2] https://en.wikipedia.org/wiki/Henry_Paynter
[3] Application Manual for Operational Amplifiers
December 1965, Philbrick / Nexus Research, Dedham, MA
Article By: Steve Hageman / www.AnalogHome.com
We design custom: Analog, RF, and Embedded systems for a wide variety of industrial and commercial clients. Please feel free to contact us if we can help with your next project.
Note: This Blog does not use cookies (other than the edible ones).
No comments:
Post a Comment