Histogram test and THD measurement of high resolution( 18 to 20 bits) ADCs require a sinusoidal source with THD 140 dBc Bench top generators can be used, but they are bulky The alternatives are to use a band pass filter to clean up a medium accuracy(~ 80 dBc) sinusoid from a DAC or to use a sinusoidal oscillator In either case, a very low distortion filter core is essential This work investigates techniques for realizing ultra low distortion band pass filters and sinusoidal oscillatorsĪctive RC filters have a very low distortion because nonlinearities can be suppressed using a high loop gain The main sources of distortion in an active RC bandpass filter are ( The nonlinearity of the output stage of the opamp used in the active filter coupled with the capacitance at the input of that stage This is suppressed using a buffer between the first and the second stage of the opamp ,( distortion contributed by passive components(integrating capacitors) in the feedback loop that is not suppressed by the loop gain This is mitigated using distortion cancellation, and ( output conductance nonlinearity of the opamp This is suppressed using a gain boosted cascode output stage In oscillators, an additional distortion source is the modulation of the oscillator’s loss by the ripple in the output of the amplitude stabilization loop that is required for stable sinusoidal oscillations A four phase full wave rectifier combined with second order ripple filtering minimizes this effect The Event was held virtually on WebEx platform from 3.30 pm on 1 st April, 2023. Nagendra Krishnapura, Department of Electrical Engineering, IIT Madras has delivered the lecture on “Design of Ultra low distortion Band pass Filters and Sinusoidal Oscillators”. The frequency response of the final filter (with \(f_c=0.1\) and \(b=0.08\)) is shown in Figure 4.IEEE SSCS Kolkata Chapter has successfully organized a Distinguished Lecture Program on 1 st April. The values for \(f_c\) and \(b\) in this article were chosen to make the figures as clear as possible. Hence, for a sampling rate of 10 kHz, setting \(b=0.08\) results in a transition bandwidth of about 800 Hz, which means that the filter transitions from letting through frequencies to blocking them over a range of about 800 Hz. As for \(f_c\), the parameter \(b\) should be specified as a fraction of the sampling rate. Setting \(N=51\) above was reached by setting \(b=0.08\). This is not really required, but an odd-length symmetrical FIR filter has a delay that is an integer number of samples, which makes it easy to compare the filtered signal with the original one. With the additional condition that it is best to make \(N\) odd. To keep things simple, you can use the following approximation of the relation between the transition bandwidth \(b\) and the filter length \(N\), The final task is to incorporate the desired transition bandwidth (or roll-off) of the filter. ![]() The central part of a sinc filter with \(f_c=0.1\) is illustrated in Figure 1.įigure 3. For example, if the sampling rate is 10 kHz, then \(f_c=0.1\) will result in the frequencies above 1 kHz being removed. The cutoff frequency should be specified as a fraction of the sampling rate. The impulse response of the sinc filter is defined as The sinc function must be scaled and sampled to create a sequence and turn it into a (digital) filter. The windowed-sinc filter that is described in this article is an example of a Finite Impulse Response ( FIR) filter. And, since multiplication in the frequency domain is equivalent with convolution in the time domain, the sinc filter has exactly the same effect. Multiplying the frequency representation of a signal by a rectangular function can be used to generate the ideal frequency response, since it completely removes the frequencies above the cutoff point. This is because the sinc function is the inverse Fourier transform of the rectangular function. When convolved with an input signal, the sinc filter results in an output signal in which the frequencies up to the cutoff frequency are all included, and the higher frequencies are all blocked. The sinc filter is a scaled version of this that I’ll define below. The sinc function ( normalized, hence the \(\pi\)’s, as is customary in signal processing), is defined as Theoretically, the ideal (i.e., perfect) low-pass filter is the sinc filter. How to create a simple low-pass filter? A low-pass filter is meant to allow low frequencies to pass, but to stop high frequencies. ![]() This article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below, and download the resulting filter coefficients. Summary: This article shows how to create a simple low-pass filter, starting from a cutoff frequency \(f_c\) and a transition bandwidth \(b\).
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