Analog Computers

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Transistor Switches in Analog Computing Circuits

This document is a translation of the original German-language article “Der Transistorschalter im analogen Rechenkreis” (1966).

Title Page (p. 1)

Transistor Switches in Analog Computing Circuits Transistor switches in analog computing circuits

by E.V. GILLES and H. SCHUCHMANN Rechenmaschinen-Laboratorium, Technische Hochschule Stuttgart

Elektron. Rechenanl. 8 (1966), No. 2, S. 186–189 Received: 11 January 1966

Abstract (German): To solve partial differential equations by the analog method, transistor switches are needed that rapidly switch individual computing elements into and out of the analog network. In this paper the functioning and switching behavior of such transistor switches is described. The input-output circuit consists of a transistor in emitter follower configuration.

(English abstract already provided on the title page)

1. Requirements for Transistor Switches (p. 2)

The transistor switch must simultaneously meet several electrical requirements. The switching process between the two states — conducting and blocking — must occur with sufficient speed. In addition, when in the conducting (closed) state, the switch should have as low a resistance as possible, and when in the blocking (open) state, as high a resistance as possible. The residual (“leakage”) current of the transistor in the blocked state must be correspondingly low.

The transistor switch is used in analog computing circuits to connect or disconnect elements (integrators, amplifiers) from the network. Figure 1 shows the use of transistor switches:

  • (a) Switch at the output of a summer
  • (b) Switch at the input of an integrator (with integration capacitor)

Figure 2 shows a transistor switch in an analog computing network. The control signal (from 0 V to a negative switching voltage) is applied to the transistor base via a resistor.

Requirements on the Transistor Switch

Since the transistors must switch both positive and negative voltages (the computing signals range from approximately −E to +E, where E ≈ 10 V), the switch must handle both polarities. Since a single transistor can only conduct effectively in one direction, a complementary arrangement (using both npn and pnp transistors) is required for bipolar operation.

2. Properties of the Transistor Switch (p. 2–3)

The transistor acts as a voltage-controlled resistance. In the conducting state (“on”), the collector-emitter voltage drop should be as small as possible relative to the signal amplitude. In the blocking state (“off”), the leakage current (ICEO or ICES) must remain negligible.

The key parameters discussed are:

  • UCE(sat): Collector-emitter saturation voltage (ideally zero in the closed state)
  • ICEO: Collector-emitter cutoff current (leakage in blocked state)
  • fT: Transistor transition frequency (determines switching speed)

For the dynamic switching behavior, the transistor is described by its hybrid-π model. The equations relate base current, collector current, and junction capacitances. The storage time constant τS is of particular importance — it determines how quickly a transistor can be turned off after saturation.

The key equations from the text:

  • Forward current gain: hFE = IC/IB
  • Storage time: related to charge stored in base region
  • Turn-off delay: τ_off depends on minority carrier lifetime in the base

3. Transistor Parameters (p. 3–4)

The article presents measured switching characteristics for a specific transistor type. Figure 3 shows the transistor output curves (IC vs. UCE for various IB values) at low collector voltages — the saturation region is emphasized.

Figure 4 shows the measured IB–UCE characteristic curves for the transistor type examined, illustrating the relationship between base drive and saturation behavior.

The article notes that for small-signal transistors commonly used in analog computers (where signal swings are ±10 V), the required parameters are:

  • Low saturation voltage: UCE(sat) < a few hundred millivolts
  • Low leakage: ICEO on the order of nanoamperes
  • Adequate bandwidth for the switching speeds required

The transition frequency fT of the transistors must be sufficiently high so that the switching transient does not distort the computing signals. For frequencies up to approximately 1 MHz (as encountered in iterative analog computation), the transistors must switch cleanly within the computation cycle.

Figure 5 shows the measured frequency behavior of a transistor switch, demonstrating the usable bandwidth.

4. Switching Circuits (p. 4–5)

The practical switching circuit described uses transistors in an emitter-follower (common collector) configuration for the input/output interface. This arrangement offers:

  • High input impedance (minimizes loading of the computing network)
  • Low output impedance (can drive subsequent stages)
  • Voltage gain close to unity (does not distort signal amplitude)

Figure 6 shows the basic transistor switch circuit. The control logic drives the base of the switching transistor. A complementary pair (npn + pnp) handles both signal polarities.

Figure 7 shows the complete circuit for a transistor switch in an analog computer, including:

  • The switching transistor pair (complementary)
  • Base drive resistors
  • Protective diodes to clamp voltage swings
  • Interface to the control logic (typically TTL levels at the time)

The article discusses the importance of matched transistor pairs and the trade-off between switching speed and leakage current.

Figure 8 shows the reduction of residual offset voltage achievable with careful circuit design and component matching.

5. Summary / Conclusion (p. 5–6)

The transistor switch described in the article can be realized with small dimensions and is suitable for use in medium-speed analog computers solving partial differential equations iteratively. The switch achieves:

  • Sufficiently low on-resistance for the computing accuracy required
  • Sufficiently low leakage current
  • Switching times compatible with repetition rates up to approximately 1 MHz

A comparison table on the final page lists the key parameters (on-resistance, off-leakage, switching time) for the transistor switch described, alongside reference values from the literature, including results from Perel’man (1963), Hannauer (1965), and EAI Report No. 910 (April 1964).

The article concludes that transistor technology of 1966 is adequate for moderate-speed iterative analog computation, and outlines the parameters that must be specified when selecting transistors for this application.

References (p. 6):

  • Perel’man, J.J. (1963): Long-period behavior of junction transistors. Proc. IEEE 51 (Mar. 1963).
  • Boger, K.J.: Junction transistors used as switches. Transistors I, p. 56, Control and Electronics (Nov. 1963).
  • Hannauer, G. (1963): Characteristics and applications of electronic switches for analog computers. Elektronische Rechenanlagen 27 (Jun. 1965).
  • Schuchmann, H.: Diplomarbeit, Rechenmaschinen-Laboratorium, Technische Hochschule Stuttgart (Jan. 1966).
  • N.N.(1): Technische Information No. 11, Telefunken E (undated).
  • EAI Report No. 910 (April 1964).
  • EAI Digital Analog Simulator, Analog Methods (Mar. 1963).
  • Schuchmann H. [4] (Jan. 1966).

[Translation covers all 6 pages of this article; the translation is complete.]