Active Filters in the Analog Channel of a Seismic Section Plotter
Abstract Generated abstract
This paper addresses the design of compact frequency-selective filters for the analog channel of a seismic section plotter, where conventional LC filters create difficulties in size, matching, load dependence, and multichannel reproducibility. It compares active filter types and argues for active RC filters using limited-gain voltage amplifiers with Butterworth approximation, implemented as cascaded second-order high-pass and low-pass sections with selectable cutoff frequencies and slopes. A calculation and experimental adjustment procedure is proposed to reduce discrepancies between computed and actual cutoff frequencies and to correct shifts introduced by cascading stages. The developed filters provide specified seismic cutoff ranges, passband nonuniformity within 3 dB, and nonlinear distortion of about 0.25 to 0.30 percent at an 8 V input.
Full Text
Active Filters of the Analog Channel of a Seismic Section Plotter
Yu. M. Achkasov, V. B. Terekhin, V. V. Timofeev,
V. N. Sorokin, S. S. Krykin, A. E. Patrakhin
(Presented by the Scientific and Technical Seminar of the Research Institute of AEM)
At present, universal digital computers are widely used for processing seismic information. To convert discrete information obtained after processing on a digital computer into a form convenient for further interpretation, special output devices are used—seismic section plotters (SSP).
The signal from the output of the digital computer is fed to the input of a digital-to-analog converter (DAC), where it is converted into a stepped signal. In such a signal, along with the fundamental harmonics, there are high-frequency components. In addition, in a seismic signal, along with useful signals, there are signals with frequencies that carry no information, and their level must be attenuated relative to the useful signal, i.e., frequency selection must be performed. This role is performed by filters. The existing filters in seismic-prospecting equipment manufactured by industry are separately controlled \(LC\)-filters for upper and lower frequencies (high-pass and low-pass filters).
The requirement for a large set of frequency characteristics, and also the fact that the frequency spectrum of the useful seismic signal contains frequencies from 20 to 100 Hz, leads to a contradiction between the dimensions of the filters and the portability requirements for seismic equipment.
The transmission coefficient of \(LC\)-filters in the passband depends on the load resistance, cutoff frequency, and steepness. Obtaining identical transmission coefficients in the passband of filters for different cutoff frequencies and steepness requires matching the wave impedance of the filters with the load resistance, which is difficult.
In the case of multichannel equipment, obtaining identical AFC and PFC in \(LC\)-filters is a rather labor-intensive task, since chokes with completely identical inductances are required.
All the reasons listed above make urgent the problem of creating small-size filters with a large number of sets of frequency characteristics, with a uniform, flat part of the AFC in the passband, whose transmission coefficient would not depend on the cutoff frequency and load. The cutoff level of different frequencies of both the high-pass and low-pass filters should be at the same level regardless of the frequency and steepness of cutoff. Filters
must have flexibility in adjustment of the AFC and PFC. The above-listed requirements for filters can be satisfied by using active \(RC\) filters. As a rule, these devices consist of \(RC\) networks in combination with an active element implemented with transistors.
At present there are many variants of active filters, which, according to the type of active element, are subdivided into:
1) converter filters (negative-resistance converters);
2) gyrator filters;
3) filters based on operational amplifiers;
4) filters based on amplifiers with a limited gain factor.
Filters based on converters have low parameter stability, i.e., the AFC is sensitive to instability of the circuit elements. At present, converters are inferior in stability to \(LC\) filters.
Filters based on gyrators require a considerable number of active elements and are justified when micromodules are used. Filters based on operational amplifiers have an AFC that is closest to that of an ideal filter, since various transfer functions can be modeled on the basis of operational amplifiers; therefore, it is obvious that with their aid the required form of the AFC can also be obtained. The drawback of these filters lies in the difficulty of implementing simple operational amplifiers.
The simplest are filters constructed on the basis of amplifiers with a limited gain factor, current amplifiers, and voltage amplifiers. They make it possible to obtain filters with a sufficiently large cutoff slope. Filters based on voltage amplifiers, compared with current amplifiers, allow substantial input signals without distortion.
It is known that the most rational limits for changing the slope of the left and right cutoffs for seismic filters are from 10 to 36–40 dB/octave. On this basis, the slope of the left and right cutoffs should be as follows:
small slope, 10 dB/octave — SS;
medium slope, 20 dB/octave — MS;
large slope, 40 dB/octave — LS.
In our case the cutoff frequencies of the filters are taken close to those existing in \(LC\) filters, but in accordance with the metrological requirements developed by the International Electrotechnical Commission (IEC) and the CMEA Permanent Commission for Standardization. Therefore the high-pass filters have cutoff frequencies of 20; 31.5; 50; 71.5; 100 Hz, and the low-pass filters—25, 40, 63, 80, 112 Hz. The cutoff frequencies are determined at a level of 3 dB below the maximum signal level.
Comparing the existing types of active filters, and also on the basis of the requirements imposed on seismic filters, we come to the conclusion that, for constructing seismic active filters, the most acceptable are filters based on voltage amplifiers with a limited gain factor and with Butterworth approximation, since they have a comparatively uniform flat AFC in the passband and a linear PFC in the attenuation band.
The required slope of the filters is realized by series connection of four second-order filters with a slope of 10 dB/octave for each cascade. In order that the filter characteristics not depend on the internal resistance of the preceding block (DAC), an emitter follower (EF) is placed at the input of the filters. The block diagram of the filters is pre-
is shown in Fig. 1,a. As the active element of the filters, a composite emitter follower (CEF) is used, built with transistors of different conductivity types (MP10B and MP115). The use of such a CEF makes it possible to obtain a voltage gain of the active element greater than unity if the resistance \(R_4\) is included (Fig. 1,b, c). The DC operating mode of the low-pass filters is set either by the CEF input or by the DC component of the high-pass filter, depending on the operating mode.
Fig. 1. \(a\)—block diagram of the filters; \(b\)—low-pass filter cascade; \(c\)—high-pass filter cascade
Existing calculation methods give a discrepancy between the calculated cutoff frequency and the experimental one of up to 30%. To obtain greater accuracy in the cutoff frequency of the filters, we propose the following procedure:
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It is advisable to begin calculating the filter parameters from the lowest cutoff frequency.
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We determine the value of the input resistance of the composite emitter follower
\(R_{\mathrm{in}} \approx \beta_1 \cdot \beta_2 (R_3 + R_5)\), where \(\beta_1\) and \(\beta_2\) are the current gain coefficients of the transistors. -
For high-pass filters, we set the resistance value
\[ R_2 \leq \frac{1}{(20 \div 40)} R_{\mathrm{in}}. \tag{1} \]
- We determine the resistance value \(R_1 \approx \dfrac{1}{(10 \div 20)} R_2\). It is known [1] that a filter can be represented as a section with natural frequency
\[ \frac{1}{\omega_0}\sqrt{R_1 \cdot R_2 \cdot C_1 \cdot C_2}. \tag{2} \]
Let \(C_1=C_2\); then from formula (2) the capacitance value can be determined as
\[ C=\frac{1}{2\pi f_0\sqrt{R_1\cdot R_2}}. \tag{3} \]
As an approximation, it is assumed that the natural frequency of the filter corresponds to the required cutoff frequency of the filter, i.e. \(f_0 \approx f_{\mathrm{cr}}\).
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We construct the experimental amplitude–frequency characteristic for the above-determined filter parameters. By selecting the resistance \(R_3\), we ensure that the AFC in the passband either has no, or has only the minimally possible, magnitude \(\delta \to 0\) (Fig. 2,a), proceeding from the specified cutoff steepness.
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From the experimental AFC, the actual cutoff frequency is determined at the level taken from the condition of obtaining its specified nonuniformity. Let the experimental characteristic have the form shown in Fig. 2,a, where \(f_{\mathrm{cr.e}}\) is the experimental cutoff frequency, which differs from the natural frequency of the filter by the amount
\[ K_1=\frac{f_{\mathrm{cr.e}}}{f_0}. \]
Fig. 2
- Since the experimental characteristic differs from the required one, it must be shifted to the left or to the right; for this purpose a refined calculation is carried out:
a) from the required limiting cutoff frequency we determine the natural frequency of the filter
\[ f_0=\frac{f_{\mathrm{cr}}}{k_1}; \]
b) from formula (3) we determine the value
\[ \frac{1}{\sqrt{R_1R_2}}=2\pi f_0 C; \]
c) from relation (1) we determine the value \(R_1\) or \(R_2\). The calculation of low-frequency filters is carried out analogously, but under the following conditions:
\[ R_1=R_2 \quad \text{and} \quad C_2 \approx \frac{1}{5}C_1. \]
When developing subsequent stages of the high-frequency filter and low-frequency filter, it is necessary to take into account that, in general, the filter is a series connection of individual sections; consequently, the overall transfer function is determined by the product of the individual transfer functions of the sections
\[ W_{\Sigma}=W_I\cdot W_{II}\cdot W_{III}\cdot W_{IV}. \]
If this is represented on a logarithmic scale, we shall have
\[ \Sigma LH(f) = LH(f)_{\mathrm{I}} + LH(f)_{\mathrm{II}} + LH(f)_{\mathrm{I}} + LH(f)_{\mathrm{IV}}. \]
If the parameters of the elements of the second filter stage are made exactly the same as those of the first, then \(LH(f)_{\mathrm{II}}\) will coincide with \(LH(f)_{\mathrm{I}}\), and the overall logarithmic characteristic (LAFC) \(\Sigma LH(f)_{\mathrm{I}}\) will have the form shown in Fig. 2,b. As can be seen, the resulting cutoff frequency \(f_{\mathrm{cr}.2}\) has deviated from the specified cutoff frequency \(f_{\mathrm{cr}.1}\); therefore \(LH(f)_{\mathrm{II}}\) must be shifted to the left so that \(\Sigma LH(f)_{\mathrm{I,II}}\) has the same cutoff frequency as \(LH(f)_{\mathrm{I}}\) (Fig. 2,c). The parameters of the subsequent stages are calculated in an analogous manner, but with their own correction coefficient \(k_i\), which takes into account the shift of the LAFC of the given stage relative to the preceding one.
Fig. 3. \(a\) — experimental amplitude-frequency characteristics of the high-frequency filters; \(b\) — experimental amplitude-frequency characteristics of the low-frequency filters.
—— small steepness;
— — — medium steepness;
— · — large steepness.
The filters developed have the AFC shown in Fig. 3,a, b.
Boundary cutoff frequencies:
HFF — 20; 31.5; 50; 71.5; 100 Hz;
LFF — 25, 40, 60, 80, 112 Hz.
The cutoff frequencies are taken at the level of 2.5 dB. The nonuniformity of the frequency response does not exceed 3 dB. Nonlinear distortion at the maximum input signal of 8 V is no more than 0.25–0.30%.
References
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A. E. Znamensky, I. N. Teplyuk. Active RC Filters. “Svyaz,” 1970.
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Yu. M. Achkasov, V. B. Terekhin, V. N. Sorokin. The analog channel of an input device for universal electronic digital computers. Reports of the VII Scientific and Technical Conference. Static Converters in Automation and Electric Drives. TSU Publishing House, Tomsk, 1971.