PHOTORESISTOR AND INCANDESCENT BULB AS A CONTROLLED ELEMENT OF AN ELECTRIC CIRCUIT

M. S. ROITMAN, B. A. PERMINOV, E. I. TSIMBALIST, N. P. FEFYLOV

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

The difficulty of solving various problems in the measurement, stabilization, or regulation of voltages, currents, frequency, phase, and other parameters is determined to a significant degree—and often chiefly—by the characteristics of the controlled element. Modern technology possesses a very extensive arsenal of electrically controlled elements (electron-tube, semiconductor, magnetic, dielectric). However, few of them can be directly included in an alternating-current circuit without altering the voltage spectrum. In other words, the number of elements that are linear with respect to the controlled circuit is small. But the list of elements narrows still further when, along with the requirements of linearity, there is also the requirement that the resistance be independent of the instantaneous values of the controlling factor, as well as linearity with respect to the controlling circuit. In practice, under known limitations, only thermistors and metallic resistance thermometers with indirect heating, as well as incandescent bulbs in combination with photoresistors, satisfy these requirements.

The properties of circuits with thermistors have been set forth quite fully in the literature, in particular in [1]; data on domestically produced thermistors are also given there. However, thermistors with indirect heating, along with their known positive properties, also have a number of disadvantages, the chief of which are a considerable dependence on the temperature of the surrounding medium and high inertia (for TKP-300 the time constant is 13.5 sec, for TKP-20—143 sec). Metallic resistance thermometers with indirect heating [2] have these disadvantages to a much lesser degree, but their relative transfer coefficient is small and, most importantly, they are not manufactured industrially.

In recent years, owing to the appearance of incandescent bulbs with rated currents on the order of tens of mA and voltages on the order of a few volts, as well as photoresistors that are sufficiently stable over time and with temperature and that have a large ratio of conductivity change with illumination, it has become possible to create very sensitive electrically controlled elements. Some possible applications of such elements have been reported in [3, 4], etc.; however, as far as the authors know, sufficiently complete characteristics of such elements are not available, which does not make it possible to judge clearly their applicability for solving one or another specific technical problem, nor the fundamental possibilities they can provide.

The authors of the present work carried out investigations of the characteristics of controlled elements based on incandescent bulbs (MIN-1, MIN-3, “Tesla”) and low-resistance cadmium-sulfide photoresistors (PR) of the SF2-2 and FSK-2N types. The results of these investigations are set forth below.

Transfer coefficient. By the relative transfer coefficient of a controlled element we shall mean the ratio of the relative change in the output parameter (in our case, the resistance of the PR, \(R_\phi\)) to the relative change in the input parameter. Depending on the operating mode, the input parameter is either the current \(I_l\) or the voltage \(U_l\) across the bulb. Thus, we shall distinguish the relative current transfer coefficient \(K_i\) and voltage transfer coefficient \(K_u\):

\[ K_i = \frac{\dfrac{\Delta R_\phi}{R_\phi}} {\dfrac{\Delta I_l}{I_l}}, \qquad K_u = \frac{\dfrac{\Delta R_\phi}{R_\phi}} {\dfrac{\Delta U_l}{U_l}} \]

Figure 1 gives the averaged dependences \(R_\phi=f(I_l)\) for 4 specimens of SF2-2 and 8 specimens of FS-K2N before and after aging. As

Fig. 1. 1—FS-K2N and MIN-3 before aging; 2—the same after 1400 hours of aging; 3—SF2-2 and “Tesla” bulb before aging; 5—the same after 400 hours of aging; 6—SF2-2 and MIN-3 before aging; 4—SF2-2 and MIN-1 before aging.

is evident from the figure, the resistance of the illuminated PR, \(R_{\text{ill}}\), in combination with the “Tesla” bulbs (6 V, 0.05 A) and MIN-1 (18 V, 0.075 A) is approximately \(1\ \text{k}\Omega\); in combination with the MIN-3 bulb (2.5 V, 0.16 A) the resistance decreases to \(200\text{–}300\ \Omega\). The dark resistance of the PR, \(R_t\), is usually of the order of \(10^8 \div 10^9\ \Omega\). Thus, the multiplicity

the range of resistance variation,

\[ \gamma=\frac{R_m}{R_{\text{illum.}}} \]

has a value of \(10^6\) and higher, and considerably exceeds the rated data for the photoresistors.

In a number of cases, when analyzing circuits with a controlled element, it is necessary to know the analytical expression of the function \(R_\phi=f(U_l)\), or \(R_\phi=f(I_l)\). In approximating the characteristics one may use functions such as:

\[ R_\phi=R_\infty e^{\frac{a}{U_l}}, \qquad R_\phi=\frac{b}{U_l+c}, \quad \text{etc.} \]

Here \(U_l\) is the voltage across the incandescent bulb,
\(R_\infty\) is the value of the PR resistance at \(U_l=\infty\),
\(a,b,c\) are constants.

For example, for an SF2-2 photoresistor and a “Tesla” bulb, the dependence of resistance on the voltage across the bulb in the range from 2.5 to 6 V (30–50 mA), after aging, is well represented by the following function (with an error of \(\pm 10\%\)):

\[ R_\phi=180 e^{\frac{10.8}{U_l}}. \]

From this it is not difficult to obtain an expression for the relative voltage transfer coefficient

\[ K_u=-\frac{10.8}{U_l}. \tag{1} \]

For MIN-3 and FSK-2N, after 1400 hours of aging, the dependence \(R_\phi=f(U_l)\) in the range \(U_l=0.8\div 1.6\) V is approximated by the expression

\[ R_\phi=420 e^{\frac{4.5}{U_l}} \]

(with an error of \(\pm 10\%\)). In this case:

\[ K_u=-\frac{4.5}{U_l}. \tag{2} \]

The minus sign in both cases indicates a decrease in the resistance of the PR as the voltage across the bulb increases. The relative current transfer coefficient can be expressed through \(K_u\) as follows: \(K_i=n_i\cdot K_u\), where \(n_i\) is a coefficient determined from the averaged current-voltage characteristics of the bulbs (Fig. 2). According to Fig. 2, for “Tesla” bulbs (curve 1),

\[ I_l=6.15(2.4+U_l), \]

for MIN-3 bulbs (curve 2),

\[ I_l=38(1.35+U_l). \]

Expressing the voltage in terms of the current, we obtain:

\[ (K_i)_{\text{tesla}}=-\frac{66.5\cdot I_l}{(I_l-14.5)^2}, \tag{3} \]

\[ (K_i)_{\text{min-3}}=-\frac{171\cdot I_l}{(I_l-51.3)^2}. \tag{4} \]

Here \(I_l\) is the bulb current in mA.

The dependences \(|K_u|=F(I_l)\) and \(|K_i|=\Phi(I_l)\), constructed from formulas (1–4), are shown in Fig. 3.

From consideration of Fig. 3, the following may be concluded:

1. In the constant-current mode, the transfer coefficient \(K_i\) is greater than in the constant-voltage mode \(K_u\). This is associated with the Barretti effect—

… in incandescent bulbs. The latter is clearly illustrated by the current–voltage characteristics of the bulbs. For example, for the “Tesla” bulb, a change in current \(I_l\) from 30 mA to 35 mA, i.e., by approximately 17%, corresponds to a change

\[ \frac{\Delta U_l}{U_l}=33\%. \]

Fig. 2. 1 — “Tesla”; 2 — MIN-3 after aging, 3 — MIN-3 before aging, 4 — MIN-1.

1. The maximum transfer coefficient (about 10) occurs at small currents; as the controlling current (voltage) increases, the transfer coefficient decreases, tending toward a definite value.

Fig. 3. Dependence of the transfer coefficient with respect to current and voltage on the current of the bulbs: 1, 2 — “Tesla”; 3, 4 — MIN-3.

Nonlinearity. Linearity in the control circuit is determined by the linearity of the incandescent-lamp circuit. As is known, an incandescent lamp is an inertial nonlinear element. Its resistance is linear for alternating voltages with a frequency higher than a certain cutoff frequency \(f_{\mathrm{gr}}\), and nonlinear for lower frequencies. The value of the cutoff frequency is determined by the time constants of the lamp, as well as by the magnitude of the nonlinear distortions permissible in the particular case.

The linearity of the element in the controlled circuit is determined by the current-voltage characteristic of the photoresistors. The linearity of the latter is observed up to considerable electric fields, after which it is violated as a result of electron injection from the contacts; in this case the concentration of current carriers ceases to be constant and begins to increase with increasing electric field. However, in the region of low voltages (on the order of tens of mV), photoresistors possess noticeable nonlinearity, which is mainly due to the nonohmic nature of the contacts and, consequently, their asymmetry.

Dynamic characteristics. In the general case, the controlled element under consideration is a nonlinear aperiodic second-order link. Its transfer coefficient may be expressed in the following form:

\[ K(p)=\frac{R(I_l)}{(1+p\tau_l)\cdot(1+p\tau_f)}, \]

where \(R(I_l)\) corresponds to the operating point on the characteristics shown in Fig. 1,

\[ \tau_l \]

is the time constant of the incandescent lamp;

\[ \tau_l=\tau_n \]

during current rise and

\[ \tau_l=\tau_{\mathrm{sp}} \]

during current decay,

\[ \tau_f \]

is the time constant of the photoresistor.

The transient process in an incandescent lamp is determined by the conditions of thermal balance and, in the general case, depends on the initial values and on the magnitudes of the changes in the power consumed by the lamp. It should be noted that the nature of the transient process depends on the operating mode of the lamps. The character of the transients of the luminous flux of incandescent lamps MIN-3, MIN-1, and “Tesla” was investigated experimentally. The source of rectangular voltage was an NGPK generator; the luminous-flux meter was an FEU-1 photomultiplier. The experiments showed that the transient characteristics have a typically nonlinear character. With an initial voltage lower than the ignition voltage of the lamp, there is a delay in the transient characteristics (Fig. 4), caused by the absence of luminous flux for a certain time. As the magnitude of the voltage step increases, the delay time and the rise time of the luminous flux decrease. The time constants for rise of the luminous flux \(\tau_n\) are smaller than the decay time constants \(\tau_{\mathrm{sp}}\) for all the lamps indicated above. The \(\tau_n\) and \(\tau_{\mathrm{sp}}\) of different lamps lie within the range from tens of msec to \(0.2\div0.3\) sec. The time constant both for rise and for decay of the photocurrent for SF2-2 does not exceed 0.06 sec, and for FSK-2N, 0.1 sec. The inertia of the controlled element can be judged from the form of the amplitude-phase characteristics (AFC). The AFC for SF2-2 and a MIN-3 lamp (Fig. 5, curves 1, 2, 3, \(I_1>I_2\)) and for SF2-2 and a “Tesla” lamp (curves 4, 5, \(I_4>I_5\)) were taken using an NGPK generator and an S1-19 oscilloscope with two BPU-1 units. The curves are given on a relative scale (in oscilloscope scale divisions).

Stability of the parameters over time. To determine the stability of the pairs, the authors used photoresistors of the FS-K2N and

SF2-2 in combination with a MIN-3 bulb. Sixteen sets of pairs were made and subjected to aging. After a certain time the dependence \(R_{\phi}=f(I_{\ell})\) was recorded, from which the relative change in resistance

\[ \frac{\Delta R_{\phi}}{R_{\phi}}=\varphi(t) \]

was calculated for definite values of the current and voltage on the bulb. The stability of the pair is affected by the aging both of the bulbs and of the photoresistors. The aging process

Fig. 4. Transient characteristic of the MIN-3 incandescent bulb: downward—switching on, upward—switching off.

is very complex and is determined mainly by the evaporation of tungsten in vacuum, as well as by recrystallization of the fibrous structure of the filament. The rate of evaporation, and consequently the service life of the bulbs, depends very strongly on the temperature of the heated filament, which in turn is a function of the current \(i_{\ell}\). Experimental investigations show (Fig. 6) that during the first 100–200 hours intensive aging takes place, caused mainly by recrystallization of the filament, and thereafter, provided that the bulb current is 10–20% below nominal, the parameters of the bulbs become very stable. The service life of MIN-3 bulbs at 10% underheating is about 7000 hours and increases sharply as the current is reduced.

Fig. 5.

Aging of CdS photoresistors, as indicated in [5], lasts 300–400 hours. The maximum value of the change

\[ \frac{\Delta R_{\phi}}{R_{\phi}} \]

during this time reaches 40%; subsequently the instability decreases sharply, and the change in the ratio

\[ \frac{\Delta R_{\phi}}{R_{\phi}} \]

over 7000 hours does not exceed 3–5%. Moreover, the stability of the pair as a whole during the first 300–400 hours is affected more strongly by the aging of the bulbs.

Fig. 6. Aging of the MIN-3 incandescent bulb.

Studies of aged pairs for short-term instability showed that the change in

\[ \frac{\Delta R_{\phi}}{R_{\phi}} \]

over 8 hours of continuous operation does not exceed 0.2%.

Temperature characteristics. The temperature characteristics of the controlled element are determined mainly by the temperature dependences of the photoresistors. The change in conductivity of CdS photoresistors of the SF2-2 and FS-K2N types is small in the temperature interval from \(+10^\circ\mathrm{C}\) to \(+35^\circ\mathrm{C}\). Outside this interval the TCR increases. The TCR in the temperature interval from \(0^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\) for SF2-2 is on average (for 7 samples) \(0.37\%/^\circ\mathrm{C}\), and for photoresistors of the FSK-2N type it does not exceed \(0.12\%/^\circ\mathrm{C}\).

Photo- and thermo-emf of photoresistors. To measure the photo-emf, the photoresistor was illuminated by a 220 V, 150 W incandescent lamp through a heat filter. The illumination of the photoresistor was 360 lx. The value of the photo-emf, averaged over 7 samples of SF type SF2-2, is 37 μV; the thermo-emf of SF2-2 is approximately 3.7 μV. The photo-emf of SF2-2 photoresistors when illuminated by a MIN-3 bulb is 1.5 μV, and when the current is reduced it amounts to fractions of a microvolt.

REFERENCES

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1. M. S. Roitman, V. K. Zhukov. Application of photoresistors for voltage stabilization. (Proceedings of the Second Conference). Publishing House of the Siberian Branch of the Academy of Sciences of the USSR, Novosibirsk, 1962.

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3. B. T. Kolomiets, A. O. Olesk. Characteristics of photoresistors made of polycrystalline CdS. Elektrichestvo, No. 11, 1951.