Dynamic errors of broadband Chebyshev bandpass filters switched on at the ADC input in automatic control systems

The dynamic errors of band-pass filters (BPF) of the n-th order, consisting of series-connected low-pass filters (LPF) of the Chebyshev type of the n-th order with a cutoff frequency of the amplitude-frequency characteristic (AFC) of the filter $\boldsymbol{\omega}_{\text{SH}}$ and high-pass filters (HPF) of the Chebyshev type are investigated n-th order with the cutoff frequency of the frequency response of the filter $\boldsymbol{\omega}_{\text{SH}}$. It is shown that the dynamic errors of the nth order BPF are determined by the cutoff frequency $\boldsymbol{\omega}_{\text{SH}}$ of the LPF and significantly depend on the frequency ratio $\boldsymbol{\omega}_{\text{SB}}/\boldsymbol{\omega}_{\text{SH}}$. As a result of the simulation, the delay times of the BPF were determined, which negatively affect the effective capacity of the ADC. Approximating equations for the dynamic error of the BPF as a function of the parameters $\mathbf{n}, \ \omega_{\text{SH}}$ and $\boldsymbol{\omega}_{\text{SB}}/\boldsymbol{\omega}_{\text{SH}}$ are obtained. Estimates of the maximum dynamic error for filters of the 1st, 2nd and 3rd orders, as well as the errors of the proposed approximation are given.

I. Introduction

The use of bandpass filters in analog-to-digital automatic control systems (ACS) to isolate a given spectrum of signals, for example, piezoelectric sensors [1], before their analog-to-digital conversion leads to a signal delay [2], which adversely affects the effective bit [3] depth of the ADC [4]–[8]. Options for the practical use of a bandpass filter, when it is connected to the input of the ADC in the ACS, are given in the work (Anton Patyuchenko. RF signal chain discource - part 2: Essential building block - Analog Devices vol.55, No. 3,2021).