Switch with low feedthrough
Abstract Generated abstract
This paper proposes an electromechanical commutator for single-channel phasemeters intended to reduce parasitic feedthrough when switching high-frequency input signals directly at the instrument input. The authors analyze a relay-contact switching link using equivalent T-network models for its closed and open states, derive formulas for the voltage transfer coefficient and resulting phase error, and compare one-contact and two-contact-group configurations. Calculations for commercially available relays at 100 MHz indicate that the proposed cascaded contact arrangement can greatly reduce phase error even for large input level ratios, supporting operation over a broad dynamic range. Schematic variants for single-channel and cross-channel switching are presented, and an experimental test at 30 MHz reports a closed-switch transfer coefficient better than 0.7 by 10 to the minus 5.
Full Text
A Commutator with Low Feedthrough
A. A. Shibaev, V. Ya. Supyan
(Presented by the scientific seminar of the Department of Theoretical Foundations of Radio Engineering, TIRiET)
For the construction of “single-channel” phasemeters, an electromechanical commutator is proposed that has low parasitic feedthrough in the closed state.
Calculation formulas are given for estimating the error introduced by the commutator described; schematic diagrams of several commutator variants are presented.
In recent years, the development of phase-measurement technology has proceeded along the path of designing “single-channel” measuring devices, because “single-channel phasemeters” possess a number of advantages in comparison with two-channel ones. In particular, in single-channel phasemeters, in principle there are no errors caused by instability of the frequencies of the input signals or by time-dependent hardware instabilities. In addition, in some variants of frequency-converter design it is possible to expand considerably the dynamic range of the phasemeter input signals without making additional adjustments.
One of the serially produced phasemeters, F2-4, is built according to a partially single-channel circuit; signal commutation in it is carried out at an intermediate frequency, which does not make it possible to reduce the errors arising in the two-channel part of the circuit within the dynamic range of the input signals.
The use of commutation directly at high frequency at the input of a phase-measuring device, at operating frequencies on the order of 100 megahertz and higher, is made difficult by parasitic feedthrough of the signal through the commutator in its closed state. The magnitude of the error in this case may be estimated by the formula
\[ \Delta \varphi = m \operatorname{arc\,tg} K, \tag{1} \]
where
\(K\) is the voltage transfer coefficient of the commutator in its closed state,
\(m\) is the ratio of the signal levels at the inputs of the phasemeter. The use, for channel commutation, of electronic vacuum-tube switches in the best tube samples (with a feedthrough capacitance on the order of \(0.05 \div 0.1\ \text{pF}\)), for a level ratio \(m\) on the order of 100, does not allow an error of less than \(2 \div 5\) degrees to be obtained.
In [1] a commutator implemented with semiconductor diodes at a fixed frequency of \(70\ \text{MHz}\), for a step in levels
Fig. 1. Schematic and equivalent circuits of a commutator section in the closed state
Fig. 2. Schematic and equivalent circuits of a commutator section in the open state
by a factor of 100 the error of such a commutator is about \(0.6^\circ\). In addition, the commutators described have their own frequency-dependent phase shifts, are asymmetrical, i.e., in different half-periods of commutation they introduce different phase shifts and, in principle, have amplitude-phase errors when operating over a wide range of input signals. The electromechanical commutator described below is free of the listed shortcomings.
The basic element of the commutator is a link consisting of two contact groups of two electrical relays connected in cascade; moreover, each of the contact groups consists of series-connected closed (open) and open (closed) contacts. To eliminate capacitive coupling between the cases and the contacts of the two relays, a cable insert is used in the link.
The schematic and equivalent circuits of the commutator link in the closed and open states are shown in Figs. 1 and 2, respectively. In the closed state, switches \(K_1\) and \(K_4\) are open, and switches \(K_2\) and \(K_3\) are closed.
In the equivalent circuits (Figs. 1, \(в\), and 2, \(в\)) the following notation is introduced:
\(C_{\text{k}}\) and \(C'_{\text{k}}\)—capacitances of the open relay contacts,
\(L_{\text{k}}\) and \(L'_{\text{k}}\)—self-inductances of the contacts,
\(r_{\text{k}}\) and \(r'_{\text{k}}\)—active resistances of the closed contacts,
\(C_{\text{p}}\)—parasitic capacitance between the input and output of the two contact groups. In practice, with a cable-insert length of \(5\)–\(7\) cm, the capacitance \(C_{\text{p}}\) can be neglected.
The voltage transfer coefficient of a T-shaped four-terminal network loaded by resistance \(Z_{\text{n}}\) is determined by the expression
\[ \dot{K}=\frac{1}{a_{11}+\dfrac{a_{12}}{Z_{\text{n}}}} =\frac{Z_2\cdot Z_{\text{n}}}{(Z_1+Z_2)(Z_3+Z_{\text{n}})+Z_1Z_2}. \tag{2} \]
For the closed state of the commutator (Fig. 1, \(a\)), in equation (2) one may set \(Z_1 \gg Z_2\), \(Z_3 \gg Z_2\), \(Z_3 \gg Z_{\text{n}}\). Then we obtain
\[ \dot{K}=\frac{Z_2Z_{\text{n}}}{Z_1Z_3}. \tag{3} \]
If, for simplicity, we take \(C'_{\text{k}}=C_{\text{k}}\); \(L'_{\text{k}}=L_{\text{k}}\); \(r'_{\text{k}}=r_{\text{k}}\), then from the equivalent circuit (Fig. 1, \(б\)) we have
\[ Z_1=Z_3=\frac{1}{j\omega C_{\text{k}}} \quad \text{and} \quad Z_2=\frac{r_{\text{k}}+j\omega L_{\text{k}}}{2}. \]
The transfer coefficient in this case is equal to
\[ \dot{K}'_3=\frac{1}{2}Z_{\text{n}}(r_{\text{k}}+j\omega L_{\text{k}})\omega^2 C_{\text{k}}^2. \tag{4} \]
In the open state of the commutator, contacts \(K_1\) and \(K_4\) are closed, and contacts \(K_2\) and \(K_3\) are open (Fig. 2, \(a\)). In this case one may assume \(Z_2 \gg Z_1\); \(Z_2 \gg Z_3\); \(Z_{\text{n}} \gg Z_3\).
The transfer coefficient of the commutator in the open state from equation (2) is equal to
\[ \dot{K}_0=\frac{Z_2\cdot Z_{\text{n}}}{Z_2Z_{\text{n}}+Z_1Z_2}\simeq 1. \tag{5} \]
In the diagram: Input I; Input II; \(p_1\); \(p_2\); \(p_3\); \(p_4\); Output.
Fig. 3. Circuit diagram of a switch with switching of two inputs to a common channel.
Fig. 4. Schematic diagram of a commutator with cross switching of channels
Diagram labels: Input I; Input II; Input III; Input IV; \(p_1\); \(p_2\); \(p_3\); \(p_4\).
The error due to parasitic transmission through the closed switch can be determined from the formula
\[ \Delta\varphi_{\max}=m\operatorname{arc\,tg}\frac{K_3}{K_0}\simeq m\operatorname{arc\,tg}K_3=0.5mR_{\mathrm{n}}\omega^2C_{\mathrm{k}}^2\sqrt{r_{\mathrm{k}}^2+\omega^2L_{\mathrm{k}}^2}, \tag{6} \]
where \(R_{\mathrm{n}}\) is the load resistance, equal to the characteristic impedance of the cable used in constructing the switch.
If it is assumed that at higher frequencies \(\omega L_{\mathrm{k}}\gg r_{\mathrm{k}}\), then
\[ \Delta\varphi_{\max}=0.5mR_{\mathrm{n}}\omega^3C_{\mathrm{k}}^2L_{\mathrm{k}}. \tag{7} \]
The voltage transfer coefficient when one contact group is used, for example \(K_1\) and \(K_2\), is determined from the expressions \(K_3=\omega^2C_{\mathrm{k}}L_{\mathrm{k}}\) and \(K_0\simeq 1\). In this case the maximum error is equal to
\[ \Delta\varphi_{\max}=m\omega^2C_{\mathrm{k}}L_{\mathrm{k}}, \]
i.e., it is
\[ \frac{1}{0.5\omega R_{\mathrm{n}}C_{\mathrm{k}}L_{\mathrm{k}}} \]
times greater than when two relay contact groups are used.
For commercially produced relays of types RES-9 and RES-10, the intercontact capacitances are \(C_{\mathrm{k}}\simeq 0.2\) pf; the self-inductances of the contacts are \(L_{\mathrm{k}}\simeq 0.01\) μH. With an active load resistance \(R_{\mathrm{n}}=75\) ohms at a frequency of 100 MHz, for one contact group
\[ K_3=8\cdot 10^{-4}. \]
For \(m=1\), \(\Delta\varphi_{\max}=0.05^\circ\); for \(m=100\), \(\Delta\varphi_{\max}=50^\circ\). As can be seen, the use of one contact group at large differences in input-signal levels is impermissible because of the large error due to parasitic transmission.
For the switch element (Fig. 1, \(a\))
\[ K_3=0.18\cdot 10^{-5},\qquad \Delta\varphi_{\max}=m\cdot 0.18\cdot 10^{-5}\ \mathrm{rad}. \]
\[ \text{For }m=1\quad \Delta\varphi_{\max}=0.00012^\circ; \]
\[ \text{for }m=100\quad \Delta\varphi_{\max}=0.012^\circ. \]
Thus, the switch element considered can be used to construct a “single-channel” phasemeter with switching of the input signals directly at high frequency over a wide (up to 60–80 dB) dynamic range and with arbitrary level ratios. It should be emphasized that one further advantage of the switch being described is that it is, in principle, a linear system, free from amplitude–phase errors, whereas any switches implemented on nonlinear elements (both semiconductor and electrovacuum) will have substantial amplitude–phase errors over the dynamic range.
Figures 3 and 4 show schematic diagrams of electromechanical switches with switching in one channel and with cross-switching of channels, respectively. The switch in Fig. 3 can be made using four relays of type RES-10, each having one contact group; the switch in Fig. 4 is made using four relays of type RES-9, each having two contact groups.
Experimental testing of the latter switch at a frequency of 30 MHz showed that the transfer coefficient of the closed switch is better than \(0.7\cdot 10^{-5}\).
REFERENCES
- Yu. R. Nosov. Semiconductor pulse diodes. “Sovetskoe radio,” Moscow, 1965.