Analysis of Input Circuits in the Seismic Information Reproduction Path
Abstract Generated abstract
This paper analyzes input circuit configurations for reproducing seismic information from magnetic tape using a low-resistance universal magnetic head. It compares transformer coupling, open-circuit operation, short-circuit operation, and an intermediate capacitive-coupled mode, arguing that transformers are impractical for multichannel low-frequency seismic playback because of size, resonance, pickup, and matching requirements. The authors show that a common-base input stage can approximate short-circuit conditions, improving selectivity and signal-to-noise performance while providing substantial gain, and derive expressions for input impedance and conductance with negative feedback. They conclude that frequency-dependent feedback effectively lowers input impedance, increases the equivalent coupling capacitance, and shapes the preamplifier response, making an intermediate mode close to short-circuit operation preferable in practice.
Full Text
ANALYSIS OF INPUT CIRCUITS IN THE SEISMIC INFORMATION PLAYBACK PATH
Yu. M. Achkasov, L. I. Ukhanov
The efficiency of playback of seismic information and of subsequent amplification of the signal from magnetic tape depends in many respects on the parameters of the input stage and preamplifier. In the general case, the condition for matching the signal source is the equality \(Z_i = Z_{\text{in}}\).
In our case the signal source is a seismic universal magnetic head with the following parameters:
\[ \begin{aligned} L &= 70\ \text{mH},\\ r &= 50\ \Omega,\\ f_{\text{gr}} &= 300\ \text{Hz}. \end{aligned} \]
Since the emf induced by the tape in the head is equal to
\[ e = L \frac{d\Phi}{dt} \tag{1} \]
its magnitude is directly proportional to the frequency of the signal recorded on the tape, and increases by approximately \(6\ \text{dB/oct}\). At the amplifier input there acts the voltage
\[ U_{\text{in}}=\frac{e}{Z_{\Gamma}+R_{\text{in}}}\cdot R_{\text{in}}. \tag{2} \]
Usually, to match a low-resistance magnetic head to the amplifier input, a step-up transformer is used. It provides good power matching and a sufficiently high signal-to-noise ratio. In the case of seismic recording, the use of transformers is irrational, especially in multichannel playback, since:
1) because of the low frequencies of the seismic signal, the dimensions of the transformer increase sharply;
2) parasitic resonance arises in the circuit “secondary winding — amplifier input”;
3) because the transformer is susceptible to electromagnetic pickup, special shielding and symmetrical execution of the winding center taps have to be used;
4) it is necessary to ensure identity of the transformers in multichannel playback.
For these reasons, capacitive coupling of the head to the amplifier proves preferable.
Three operating modes of the reproducing head are possible:
1) open-circuit mode;
2) short-circuit mode;
3) intermediate mode.
The open-circuit mode requires an input stage with a low noise level and a high input resistance. The disadvantage of such a stage is that, because of the high \(R_{\mathrm{in}}\), the cable’s own capacitance, connecting the head to the amplifier, has an effect; the circuit becomes susceptible to electrostatic pickups.
The short-circuit mode is more advantageous in this case, requiring \(R_{\mathrm{in}} \to 0\); then, as is evident from equation (2), as \(\omega\) increases the signal \(U_{\mathrm{in}} \to 0\), since \(Z_{\mathrm{g}}\) is inductive. Thus, in this mode partial compensation of the frequency response of the head takes place. In addition, this mode allows us to realize the selective properties of the input circuit and to improve the signal-to-noise ratio.
Fig. 1
Indeed, the quality factor of the magnetic head is \(Q = \dfrac{\omega_0 L}{r}\) (3), while the quality factor of the input circuit is \(\dfrac{\omega_0 L}{r + R_{\mathrm{in}}}\) (4), which is smaller than the quality factor of the magnetic head by a factor of \(\dfrac{r + R_{\mathrm{in}}}{r}\). It is evident that, in order to preserve a high quality factor of the input tank circuit, a very small stage resistance is required, i.e., the short-circuit mode. A mode close to it is provided by an input stage with a common base. The input resistance in this case
\[ R_{\mathrm{in}} \approx r_{\mathrm{e}} + (1-\alpha)R_{\mathrm{n}} \tag{5} \]
has a value on the order of tens of ohms, which is comparable with the head’s own resistance. The gain of the stage in this case is
\[ K_{\mathrm{i}} = \alpha \frac{R_{\mathrm{k}} \parallel R_{\mathrm{n}}}{r_i + R_{\mathrm{in}}}, \tag{6} \]
and since \(r_i\) and \(R_{\mathrm{in}}\) are small, it is not difficult to obtain \(K_{\mathrm{i}} = 100 \div 300\).
The intrinsic noise of the common-base stage is less than the noise of a follower. It is also important that the noise level is practically independent of replacing the triodes.
The head short-circuit mode requires a very large, difficult-to-implement coupling capacitance. Its value can be reduced by introducing negative feedback. Introducing feedback according to the circuit in Fig. 1 by means of \(R_{\mathrm{fb}}, C_{\mathrm{fb}}\), we obtain for the input conductance
\[ y_{\mathrm{in}\cdot\mathrm{cpl}} = \frac{i_{\mathrm{src}}}{U_{\mathrm{in}}} = \frac{i_{\mathrm{in}}+i_{\mathrm{cpl}}}{U_{\mathrm{in}}} = \frac{i_{\mathrm{in}}}{U_{\mathrm{in}}} + \frac{U_{\mathrm{in}}-U_{\mathrm{out}}}{Z_{\mathrm{cpl}}\cdot U_{\mathrm{in}}} = y_{\mathrm{in}}+y_{\mathrm{cpl}}(1-K), \tag{7} \]
since the feedback is negative, \(K=-K\), and
\[ y_{\mathrm{in}\cdot\mathrm{cpl}}=y_{\mathrm{in}}+y_{\mathrm{cpl}}(1+K), \tag{8} \]
\[ Z_{\mathrm{in}\cdot\mathrm{cpl}} = \frac{1}{y_{\mathrm{in}\cdot\mathrm{cpl}}} = \frac{Z_{\mathrm{in}}\cdot Z_{\mathrm{cpl}}}{Z_{\mathrm{in}}(1+K)+Z_{\mathrm{cpl}}}, \tag{9} \]
where
\[ Z_{\mathrm{cpl}} = \frac{1/\omega C_{\mathrm{p}}+R_{\mathrm{in}}} {\dfrac{R_{\mathrm{fb}}\cdot 1/\omega C_{\mathrm{fb}}}{R_{\mathrm{fb}}+1/\omega C_{\mathrm{fb}}}} + R_{\mathrm{in}} + \frac{1}{\omega C_{\mathrm{p}}}, \tag{10} \]
neglecting \(\dfrac{1}{\omega C_{\mathrm{p}}}\), we have
\[ K_{\mathrm{i}} = \frac{R_{\mathrm{in}}}{R_{\mathrm{in}}+R_{\mathrm{fb}}/1+R_{\mathrm{fb}}} = 1+\frac{R_{\mathrm{in}}(1+R_{\mathrm{fb}})}{R_{\mathrm{fb}}}. \tag{11} \]
Thus, there is a reduction of \(Z_{\mathrm{in}}\) by almost \(1+K\) times, which is physically equivalent to a corresponding increase in the coupling capacitance, since \(Z_{\mathrm{in}}=R+\dfrac{1}{\omega C_{\mathrm{p}}}\) and \(R=\mathrm{const}\); hence, obviously, \(C_{\mathrm{p}}\) increases.
The feedback circuit is frequency-dependent and shapes the frequency response of the preamplifier.
In pure form, neither the open-circuit mode nor the short-circuit mode is physically realizable. In our case, the input circuit operates in an intermediate mode close to the short-circuit mode, and practically realizes all its advantages.
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