Simplified calculation of the I–V characteristic of the equivalent of a lambda diode. Scheme, description

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Simplified calculation of the I–V characteristic of the equivalent of a lambda diode. Encyclopedia of radio electronics and electrical engineering

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Back in the seventies, articles began to appear in various magazines describing a very interesting element of electronic technology - the equivalent of a lambda diode (ELD). It is a specially connected pair of field-effect transistors with pn-junctions of different types and has a current-voltage characteristic (CVC) similar to the CVC of a tunnel diode, but without a second branch of positive resistance. Unlike the tunnel diode, the ELD at a voltage exceeding the turn-off voltage Uclose is closed, so that the current through it drops to several picoamperes. The ELD circuit is shown in Fig. 1, and its CVC is shown in Fig. 2.

Simplified calculation of the I–V characteristic of the equivalent of a lambda diode

With the help of ELD, it is easy to implement both circuit solutions characteristic of a tunnel diode and completely original devices, as shown in [1], [2], [3], [4]. The magazine "Radio" also addressed this topic (see [5], [6].

The wide distribution of devices based on ELDs is hindered by the complexity of calculating the I–V characteristics of an ELD using the known parameters of the field-effect transistors included in it, which in turn is determined by the complexity of approximating the I–V characteristics of a field-effect transistor [7], [8].

It is precisely because of this that formulas for calculating the main parameters of the ELD have not yet been obtained, which in most cases can be dispensed with instead of the I–V characteristics when calculating various devices on the ELD. These parameters include the maximum current through the ELD (Imax); the voltage at which this current takes place (Umax); locking voltage (Uclose); differential negative resistance of ELD (-rd); coordinates of the inflection point of the branch of the negative resistance of the VAC ELD (Uper, Iper). Having formulas that connect the ELD parameters listed above with the parameters of the field-effect transistors included in it, you can easily select the right pair of transistors, as well as calculate the generator, amplifier and any other device on the ELD.

This article describes an approximate calculation of the CVC of a symmetrical ELD and its parameters.

To obtain an approximate expression for the CVC of an ELD, we take into account that each transistor in a symmetrical ELD operates until it is completely turned off at drain-source voltages not exceeding the cutoff voltage of this transistor (and its pair, since we consider them the same). Under these conditions, the dependence of the current through the field-effect transistor on the drain-source voltage can be approximately considered linear, the voltages Usi1 \u2d Usi2 \u2d U / 1 and Usi2 \uXNUMXd UsiXNUMX \uXNUMXd -U / XNUMX are equal in absolute value, and then the CVC of the field-effect transistor can be described by a simple formula:

Ic=(Usi/Rm)(1- |Usi/2Uots|)² (1)

where Usi is the drain-source voltage of the field-effect transistor, (in the case of a symmetrical ELD, as can be seen from Fig. 1, Usi \u2d U / 0), Usi is the gate-source voltage, Uots is the cut-off voltage of the field-effect transistor, and Rm is the resistance of the field-effect transistor in the initial section of the CVC at Usi=0 in the vicinity of the point Usi=0, Ic=XNUMX:

Rm=dUci/dIc.

Such a simplified expression for the CVC of a field-effect transistor is suitable for calculating the CVC of a lambda diode when |Usi|< |Uots|. It can be seen from Fig. 1 that the CVC of the ELD is described in this case by the expression

I(U)=c(U/2)=(U/2Rm)(1-|U/2Uots|)². (2)

Considering that for a symmetric ELD |Usi|=|Uzi|, we can approximately assume

Rm=dUzi/dIc=1/Smax,

where Smax is the maximum slope of the field effect transistor, which can be taken from a reference book or measured. Then the expression for the CVC of the ELD will contain only the known parameters of field-effect transistors:

(U)=1/2 USmax(1-|U/2Uots|)² (3)

By differentiating expression (3) with respect to U, one can find the arguments for which this function has extrema.

Ue1=Uzap=2|Uots|,

which corresponds to the data from [8], where the calculation used the approximation of the CVC of a field-effect transistor by complex functions, and

Ue2=Umax=2|Uots|/3. (4)

The expression for Umax was not obtained in [8], but according to the I–V curve available there, one can see that here, too, there is a coincidence of the calculation results.

Substituting the value of Umax from (4) into (2) or into (3), we obtain

Imax=4Uots/27Rm~ 0,15Uots/Rm,

Imax=4UsSmax/27~ 0,15UsSmax.

Experiments have shown that the calculated value of Im ax differs from the experimental value for pairs of transistors KP303 and KP103, selected according to the parameters Smax and Uots, by no more than 10%. Next, you can determine the inflection point on the negative branch of the CVC, having previously found

d²I/dU²=(1/UотсRm)(3U/4U отс-1). (5)

Equating expression (5) to zero and solving the resulting equation, we determine

Uper \u4d 3Uots / XNUMX,

Iper \u2d 27Uots / 2Rm \uXNUMXd Imax / XNUMX,

which is also in good agreement with the graph from [8] and the results of experiments carried out by the author.

Next, we define

- rd=-6Rm=-6/Smax.

For an asymmetric ELD on field-effect transistors with different parameters, it is also possible to calculate the CVC using expression (2) or (3) and obtaining a system of equations, according to the method from [8], but with much simpler expressions. The agreement between the calculation results and the experimental data is quite satisfactory. Solving a system of equations is easy to carry out on any programmable calculator or computer. However, it was not possible to obtain explicit expressions for the main parameters of the asymmetric ELD.

The author expresses the hope that the ability to easily calculate the ELD parameters from the parameters of the field-effect transistors included in it will serve as an incentive for radio amateurs to create a number of devices using this promising element.

Literature

1. Kano, G. The lambda diode: versatile №egative-resistance device. "Electronics", 48(1975), no. 13, p.105-109.
2. Hodonek, Complementary field-effect transistors with a junction in a two-frequency oscillator. "Electronics", 1975, No. 22, p.60.
3. Dyakonov V.P., Semenova O.V. Switching devices on lambda transistors. "Instruments and Experimental Technique", 1977, No. 5, p.96.
4. Ptashnik I. VFO with electronic tuning. "Radio Amateur", 1993, No. 9, p.38.
5. Nechaev I. Lambda diode and its capabilities. "Radio", 1984, No. 2, p.54
6. Nechaev I. Probe-generator on the analogue of the lambda diode. "Radio", 1987, No. 4, p.49.
7. Takashi T. Approximation of function field-effect transistor characteristics by hyperbolic function, IEEE Journal of solid-state circuits. 1978, v.13, no.5, p.724-726.
8. V.I. Molotkov, E.I. Potapov. Investigation of the I–V characteristics of low-power field-effect transistors and lambda diodes and calculation of the amplitudes of an auto-oscillator based on a lambda diode. "Radioelectronics", 1991, vol. 34, No. 11, pp. 108-110.

Author: Vasily Agafonov; Publication: N. Bolshakov, rf.atnn.ru

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