Title:

United States Patent 3843880

Abstract:

A high signal-to-noise ratio (S/N) is obtainable in an apparatus for transforming luminous intensity into a voltage which is in exact inverse proportion to the luminous intensity. The apparatus is constituted by connecting a first controlling means t1 for current controlling in series to a photoconductive element Rp having non-linear characteristic of Rp = K^{.} E^{-}^{}γ, where Rp is resistance, E is luminous intensity and K and γ are constants, and by connecting a second controlling means t2 so as to receive a voltage Vp across both ends of the photoconductive element Rp and to give a signal, which is approximately proportional to Vp ^{1}^{-}^{}γ, of said first controlling means t1, which controls the current Ip of the photoconductive element Rp to be approximately proportional to the value E^{}γ^{-}^{1}, and as a result causes the voltage Vp to be approximately in inverse proportion to the luminous intensity E.

Inventors:

TSUCHIYASU K

Application Number:

05/411341

Publication Date:

10/22/1974

Filing Date:

10/31/1973

Export Citation:

Assignee:

Minolta Camera Kabushiki Kaisha (Osaka, JA)

Primary Class:

Other Classes:

250/214R

International Classes:

Field of Search:

250/206,214P,214 356

View Patent Images:

US Patent References:

Primary Examiner:

Lawrence, James W.

Assistant Examiner:

Grigsby T. N.

Attorney, Agent or Firm:

Craig & Antonelli

Claims:

What is claimed is

1. Illumination-to-voltage conversion apparatus comprising:

2. The apparatus of claim 1 wherein said second controlling means has a characteristic to produce an output signal represented by b + d^{.} log (X + r) for an input signal X, wherein b, d and r are constants.

3. The apparatus of claim 1 wherein said first controlling means comprises a first transistor having a collector electrode which is connected to said photoconductive element, said second controlling means comprising at least one second transistor having a collector electrode which is connected in series to at least one diode for logarithmic transformation and a variable resistor, the base and emitter electrodes of said first transistor being connected across the series combination of said diode and said variable resistor, and the base and emitter electrodes of said second transistor being connected across said photoconductive element.

4. The apparatus of claim 3, further including a third transistor connected in series with said photoconductive element, the base and emitter electrodes of said second transistor being connected across the series combination of said photoconductive element and said third transistor, the base electrode of said third transistor being connected to a source of reference voltage.

5. The apparatus of claim 4 wherein said second controlling means comprises two second transistors connected in series in a Darlington configuration and connected in series with at least two diodes.

6. The apparatus of claim 5 wherein said source of reference voltage comprises a potentiometer connected across said direct current source.

1. Illumination-to-voltage conversion apparatus comprising:

2. The apparatus of claim 1 wherein said second controlling means has a characteristic to produce an output signal represented by b + d

3. The apparatus of claim 1 wherein said first controlling means comprises a first transistor having a collector electrode which is connected to said photoconductive element, said second controlling means comprising at least one second transistor having a collector electrode which is connected in series to at least one diode for logarithmic transformation and a variable resistor, the base and emitter electrodes of said first transistor being connected across the series combination of said diode and said variable resistor, and the base and emitter electrodes of said second transistor being connected across said photoconductive element.

4. The apparatus of claim 3, further including a third transistor connected in series with said photoconductive element, the base and emitter electrodes of said second transistor being connected across the series combination of said photoconductive element and said third transistor, the base electrode of said third transistor being connected to a source of reference voltage.

5. The apparatus of claim 4 wherein said second controlling means comprises two second transistors connected in series in a Darlington configuration and connected in series with at least two diodes.

6. The apparatus of claim 5 wherein said source of reference voltage comprises a potentiometer connected across said direct current source.

Description:

BACKGROUND OF THE INVENTION

This invention relates to an apparatus for transforming luminous intensity to voltage wherein the voltage is in exact inverse proportion to the luminous intensity.

In general, the resistance of a photoconductive element is not in exact inverse proportion to the luminous intensity, but has the following relationship:

Rp = K^{.} E^{-}^{}γ (1)

wherein Rp is the resistance of the photoconductive element, E is the luminous intensity and K and γ are constants. Therefore, if a current Ip, which is constant irrespective of the voltage Vp across the ends of the element, is applied, then by Ohm's law, the following relationship is obtainable, wherein the voltage Vp is in inverse proportion to the γth power of the luminous intensity:

Vp = K^{.} E^{-}^{}γ Ip (2)

Hitherto, among actual apparatus requiring that an output be in exact inverse proportion to the luminous intensity, an apparatus constituted as shown in FIG. 1, wherein logarithm-transforming means such as, a logarithm-compressor circuit and a logarithm-expander circuit, is employed.

In the conventional apparatus of FIG. 1, a photoconductive element Rp is connected to a constant current source CIS so that a constant current flows through the photoconductive element Rp. The voltage Vp across the element Rp is

Vp = Rp^{.} Ip = K ^{.} E^{-}^{}γ^{.} Ip (2.1)

And is given to a logarithmic-compressor circuit LCC to produce the following output:

log Vp = -γ^{.} log E + log K ^{.} Ip (2.2)

Then the abovementioned output is applied to a multiplier circuit MC, so as to be multiplied by 1/γ to produce the following output:

(1/γ) log Vp = - log E + (1/γ)^{.} log K ^{.} Ip (2.3)

namely,

log Vp( 1/γ) = log (K^{.} Ip)(1/γ) ^{.} E^{-}^{1} ( 2.4)

the abovementioned output is then applied to an inverse logarithmic transforming circuit, i.e., a logarithmic-expander circuit LEC to produce the following output:

V' = (K^{.} Ip) (1/γ) ^{.} E^{-}^{1} ( 2.5)

wherein

V' = Vp (1/γ) (2.6)

Thus, the output V' of the logarithmic-expander circuit LEC is in exact inverse proportion to the luminous intensity E.

The abovementioned prior art apparatus has the shortcoming of having a low signal-to-noise (S/N) ratio, since noises mixed at points a or b in FIG. 1, which points are in a prior stage to the stage for the logarithmic-expansion by the circuit LEC, are expanded to a great extent by the expansion, resulting in poor signal-to-noise ratio in the output voltage V'. Hitherto, a circuit of very complicated configuration was necessary to eliminate such expansion of the noise.

SUMMARY OF THE INVENTION

This invention purports to provide an apparatus capable of attaining good S/N ratio in transforming luminous intensity to voltage with good linearity characteristic, by employing rather simple circuit constitution.

BRIEF EXPLANATION OF THE DRAWING

FIG. 1 is a schematic block diagram showing the above-mentioned conventional apparatus for transforming luminous intensity to voltage;

FIG. 2 is a schematic block diagram showing the fundamental construction of the apparatus of the present invention;

FIG. 3 is a graph showing the relationship between the input voltage and the output voltage of the second controlling means of FIG. 2;

FIG. 4 is a schematic circuit diagram showing the fundamental circuit configuration of an apparatus embodying the present invention;

FIG. 5 is a schematic circuit diagram showing one actual example of the apparatus embodying the present invention;

FIG. 6 is a schematic circuit diagram showing a circuit equivalent to the circuit of FIG. 5; and

FIG. 7 is a graph showing the relationship between the relative input luminous intensity and the relative output current flowing through the photoconductive element.

DETAILED DESCRIPTION OF THE INVENTION

The apparatus of the present invention has a fundamental configuration as shown in FIG. 2, wherein a photoconductive element Rp and a first controlling means t1, which controls the current of the element Rp, are connected in series across a D.C. power source DCS, and both ends of the photoconductor element Rp are connected to input terminals of a second controlling means t2 which applies a controlling signal to the first controlling means t1.

The first controlling means t1 controls the current Ip of the element Rp in proportion to its control input voltage Y received from the output of the second controlling means t2. The second controlling means t2 receives as an input voltage the voltage Vp across both ends of the element Rp. The output terminals "Out" are connected to respective ends of the photoconductive element Rp.

As has been explained with reference to the equations (1) and (2), the output voltage Vp is given as: Vp = K^{.} E^{-}^{}γ ^{.} Ip. Accordingly, if the current Ip is controlled to be

Ip = C^{.} E ^{}γ^{-}^{1} (3)

then, from the equations (2) and (3), the following relationship is obtainable:

Vp = K^{.} E ^{-}^{}γ ^{.} C ^{.} E^{}γ ^{-}^{1} = K ^{.} C ^{.} E^{-} ^{1} (3.1)

thus, if the relationship of the equation (3) is obtainable by means of the characteristic of the second controlling means t2, then the exact inverse proportion between the luminous intensity and the output voltage Vp is obtainable.

In order to attain the abovementioned characteristic, the second controlling means t2 should have the following characteristic between its input X and output Y:

Y = hX^{1}^{-}^{}γ (3.2)

where h is a constant. With the characteristic as abovementioned, the output Y of the second controlling means for an input voltage of Vp = KC^{.} E^{-}^{1} becomes as follows:

Y = hX^{1}^{-}^{}γ = h (KC ^{.} E^{-}^{1}) ^{1}^{-}^{}γ = K 3 ^{.} E^{}γ^{-}^{1} (3.3)

where K3 is a constant. Accordingly, the first controlling means t1 controls its output current Ip so as to be proportional to the output K3^{.} E^{}γ^{-}^{1} of the second controlling means, and therefore, the voltage Vp across both ends of the photoconductive element Rp, namely, the voltage at the output terminal OUT of this apparatus corresponds to the equation (3.1).

The characteristic of the equation (3.2) is the theoretical characteristic, which is shown by a solid curve in the graph of FIG. 3. However, it has been difficult to attain such a characteristic by means of a simple circuit. However, in practical operation, the abovementioned characteristic can be approximated by the following characteristic if constants are properly selected:

Y = b + d^{.} log (X + γ) (3.4)

The dotted curve in FIG. 3 shows the curve of the function of the equation (3.4).

The abovementioned characteristic of the equation (3.4) can be realized by utilizing a logarithmic function of a diode or diodes.

A preferred fundamental example embodying the present invention is shown in FIG. 4, wherein details of the first and the second controlling means t1 and t2 are shown. In FIG. 4, the first controlling means comprises a first transistor T1, the collector of which is connected to one end of the photoconductive element Rp. The second controlling means t2 comprises a second transistor T2, the base and the emitter of which are connected across both ends of the photoconductive element Rp, and to the collector of which are connected a diode D and a variable resistor R2 in series. The junction point p between the collector of the second transistor T2 and the diode D is for logarithmic-conversion and is connected to the base of the first transistor T1.

In general, the voltage across both terminals of a diode or diodes in series connection is proportional to the logarithm of the current flowing through the diode, and accordingly, the voltage Vpq between the points p and q is given as

Vpq = R2^{.} i + d ^{.} log i (3.3)

wherein d is a constant, and i is the current flowing through the diode D and the resistor R2.

Since the collector current Ip is proportional to the base input voltage Vpq of the transistor T1,

Ip = L^{.} Vpq = L {R2^{.} i + d ^{.} log i } (4)

wherein L is a constant. The constants L and d should be properly selected by suitably selecting circuit constants, in order to attain good approximation between the theoretical Y = X^{1}^{-}^{}γ curve and the present Y = b + d ^{.} log (X + γ) curve. Thus, the relationship of the equation (3.1) is approximated.

FIG. 5 shows a more practical embodiment provided with two variable resistors R2 and Rv as characteristic-approximation adjusting means. The apparatus also provides a pair of thermistors H1 and H2 for termperature compensation, a current adjusting transistor Q3 and a shunt resistor Bs. A Darlington connection consisting of a pair of transistors Q1 and Q2 is employed in place of the second transistor T2, in order that only very little input current to the base of the transistor Q1 is required. The transistor Q3 is provided connecting its collector, emitter and base to the positive end of the D.C. source, one end of the photoconductive element Rp, and a moving arm of the variable resistor Rv, respectively. As will be explained later, the variable resistor Rv is for adjusting the curve for good approximation in the high luminous intensity range, and the variable resistor R2 is for adjusting the curve for good approximation in the low luminous intensity range. Further, a series connection of several diodes may be employed in place of the diode D to ensure higher reverse breakdown voltage. In considering the operation, the circuit of FIG. 5 can be represented by the equivalent circuit of FIG. 6.

In FIG. 6 since both ends of the variable resistor Rv are connected across both ends of the D.C. source DCS, a divided voltage is applied to the movable contact of the variable resistor Rv and this voltage applied to the base of the transistor Q3. On account of the shunt resistor Rs, most of the emitter current of the transistor Q3 flows through the shunt resistor Rs, and accordingly, very little of the emitter current flows through the photoconductive element Rp. Accordingly, the emitter current of the transistor Q3 is little influenced by the change of the current Ip flowing through the photoconductive element Rp, ensuring a constant voltage Vo between the collector and the emitter of the transistor Q3. This voltage Vo is dependent only on the position of the moving contact of the variable resistor Rv.

The total of the abovementioned voltage Vo and the voltage Vp across the ends of the photoconductive element Rp is applied across the emitter and the base of the transistor T2, as illustrated in FIG. 6.

Now, defining the center value of the luminous intensity as Eo, the resistance and the current of the photoconductive element for this luminous intensity to be Rpo and Ipo, respectively, and the collector current of the transistor T2 and the voltage between points p and q for the abovementioned condition to be io and Vpqo, respectively, then the following relationships are given from the equations (1), (3) and (3.3):

Rpo = K^{.} Eo ^{-}^{}γ

accordingly

K = ) Rpo/Eo^{-}^{}γ (4.1)

Ipo = C^{.} Eo ^{}γ^{-}^{1}

accordingly

C = Ipo/Eo^{}γ^{-}^{1} (4.2)

By substituting the abovementioned K and C of the equations (4.1) and (4.2) into the equations (1) and (3), the following relationships are given:

Rp = K^{.} E^{-}^{}γ = (Rpo/Eo^{-} ^{}γ)E^{-}^{}γ (5)

ip = C^{.} E ^{}γ^{-}^{1} = (Ipo/Eo^{}γ^{-}^{1})E ^{}γ^{-}^{1} (5.1)

next, by defining i' as the collector current of the transistor T2 for the condition Vp = 0, on account of the linear characteristic between the base voltage Vo + Vp and collector current i of the transistor T2, the following relationship is given:

i = i' + K1^{.} Vp, (where K1 is a constant) (5.3)

Also, from the equations (3.1) and (5.3),

i = i' + K1^{.} K ^{.} C ^{.} E^{-}^{1} = i' + K2 ^{.} E^{-}^{1} (5.4)

wherein K2 = K1^{.} K ^{.} C. And accordingly,

(i - i')E = k2 (5.4)

and by applying the aforementioned condition of io for Eo in the equation (5.4),

(io - i') Eo = K2 (5.5)

from the equations (5.4) and (5.5),

i = i' + (io - i') (Eo/E) (6)

from the equations (4) and (6),

Ip = L {R2^{.} (i' + (io - i')[Eo/E]) + d ^{.} log(i' + (io - i) [Eo/E]) } (8)

for a small luminous intensity, the logarithmic term of the equation (8) is negligibly small, and accordingly, the condition i'<< (io - i) (Eo/E) is realized for a practical circuit condition. Therefore, we can express Ip as follows:

Ip ≉ L^{.} R2 ^{.} Eo ^{.} (io - i') ^{.} E ^{-}^{1} (9)

since this equation (9) has the value R2 but excludes the value Rv, the adjustment for the proximation of the curve Y = b + dlog (X + γ) to the theoretical curve Y = X^{1} ^{-}^{}γ can be made by adjusting only the variable resistor R2.

For a large luminous intensity, the logarithmic term becomes predominent and therefore, we can express Ip, as follows:

Ip =⇋ + L^{.} d ^{.} log (i' + Eo ^{.} (io - i')E^{-}^{1}) (10)

since this equation (10) does not have R2, the adjustment for the approximation can be made by adjusting only the variable resistor Rv. Namely, by adjusting the resistor Rv, the voltage Vo between the collector and the emitter of the transistor Q3 is varied, and the current i' in the equation (6) is also varied.

Thus, for both the ranges of large luminous intensity and small luminous intensity, the characteristic curve of the apparatus of FIG. 5 is well approximated to that of the theoretical curve.

From the equation (3) for the value Ipo and Eo,

Ipo = C^{.} Eo^{}γ ^{-}^{1} (10.1)

and from the equations (3) and (10.1),

Ip/Ipo = (E/Eo)^{}γ^{-}^{1} (10.2)

From the equation (3.1),

Vpo = K^{.} C ^{.} Eo^{-}^{1} (10.3)

and from the equations (3.1) and (10.3),

Vp/Vpo = (E/Eo)^{-}^{1} (10.4)

In FIG. 7 the ordinate represents values of Ip/Ipo, and the abscissa represents values of E/Eo. The solid curve indicates the theoretical characteristic which is represented by the equations (3) and (3.1) wherein γ = 0.85, while the dotted curve indicates the experimental result of the circuit of FIG. 5. In the dotted curve, the curve in the left and right parts are adjusted by the variable resistors R2 and Rv, respectively. Thus, by adjusting the variable resistors R2 and Rv, the dotted line can be well approximated to the solid line.

The apparatus of the present invention has a low noise level for the following reason:

Possible noises produced in a circuit such as illustrated in FIG. 6 takes place at the bases of the transistors. Accordingly, we should consider the noises at the bases. A small part of the noise at the base of the transistor Q3 is applied to the base of the transistor T2, since most of the emitter current of the transistor Q3 flows in the shunt resistor Rs. The noise at the base of the transistor T2 produces the noise in the current i. From the equations (2) and (4) the following relationship is found:

Vp α R2^{.} i + dlog i,

Namely, the output voltage Vp consists of a first part which is proportional to the current i and a second part which is a logarithmic compression of the current i. A noise, i.e., a small fluctuation in the current i, makes a resultant noise, i.e., a small fluctuation in the voltage Vp. Such a resultant noise consists of a first part originated from the first part R2^{.} i, i.e., a proportional part, and of a second part d log i, i.e., a logarithmic compressed part; and therefore, the resultant noise is no greater than the conventional logarithmic expanded noise as explained with reference to FIG. 1.

This invention relates to an apparatus for transforming luminous intensity to voltage wherein the voltage is in exact inverse proportion to the luminous intensity.

In general, the resistance of a photoconductive element is not in exact inverse proportion to the luminous intensity, but has the following relationship:

Rp = K

wherein Rp is the resistance of the photoconductive element, E is the luminous intensity and K and γ are constants. Therefore, if a current Ip, which is constant irrespective of the voltage Vp across the ends of the element, is applied, then by Ohm's law, the following relationship is obtainable, wherein the voltage Vp is in inverse proportion to the γth power of the luminous intensity:

Vp = K

Hitherto, among actual apparatus requiring that an output be in exact inverse proportion to the luminous intensity, an apparatus constituted as shown in FIG. 1, wherein logarithm-transforming means such as, a logarithm-compressor circuit and a logarithm-expander circuit, is employed.

In the conventional apparatus of FIG. 1, a photoconductive element Rp is connected to a constant current source CIS so that a constant current flows through the photoconductive element Rp. The voltage Vp across the element Rp is

Vp = Rp

And is given to a logarithmic-compressor circuit LCC to produce the following output:

log Vp = -γ

Then the abovementioned output is applied to a multiplier circuit MC, so as to be multiplied by 1/γ to produce the following output:

(1/γ) log Vp = - log E + (1/γ)

namely,

log Vp( 1/γ) = log (K

the abovementioned output is then applied to an inverse logarithmic transforming circuit, i.e., a logarithmic-expander circuit LEC to produce the following output:

V' = (K

wherein

V' = Vp (1/γ) (2.6)

Thus, the output V' of the logarithmic-expander circuit LEC is in exact inverse proportion to the luminous intensity E.

The abovementioned prior art apparatus has the shortcoming of having a low signal-to-noise (S/N) ratio, since noises mixed at points a or b in FIG. 1, which points are in a prior stage to the stage for the logarithmic-expansion by the circuit LEC, are expanded to a great extent by the expansion, resulting in poor signal-to-noise ratio in the output voltage V'. Hitherto, a circuit of very complicated configuration was necessary to eliminate such expansion of the noise.

SUMMARY OF THE INVENTION

This invention purports to provide an apparatus capable of attaining good S/N ratio in transforming luminous intensity to voltage with good linearity characteristic, by employing rather simple circuit constitution.

BRIEF EXPLANATION OF THE DRAWING

FIG. 1 is a schematic block diagram showing the above-mentioned conventional apparatus for transforming luminous intensity to voltage;

FIG. 2 is a schematic block diagram showing the fundamental construction of the apparatus of the present invention;

FIG. 3 is a graph showing the relationship between the input voltage and the output voltage of the second controlling means of FIG. 2;

FIG. 4 is a schematic circuit diagram showing the fundamental circuit configuration of an apparatus embodying the present invention;

FIG. 5 is a schematic circuit diagram showing one actual example of the apparatus embodying the present invention;

FIG. 6 is a schematic circuit diagram showing a circuit equivalent to the circuit of FIG. 5; and

FIG. 7 is a graph showing the relationship between the relative input luminous intensity and the relative output current flowing through the photoconductive element.

DETAILED DESCRIPTION OF THE INVENTION

The apparatus of the present invention has a fundamental configuration as shown in FIG. 2, wherein a photoconductive element Rp and a first controlling means t1, which controls the current of the element Rp, are connected in series across a D.C. power source DCS, and both ends of the photoconductor element Rp are connected to input terminals of a second controlling means t2 which applies a controlling signal to the first controlling means t1.

The first controlling means t1 controls the current Ip of the element Rp in proportion to its control input voltage Y received from the output of the second controlling means t2. The second controlling means t2 receives as an input voltage the voltage Vp across both ends of the element Rp. The output terminals "Out" are connected to respective ends of the photoconductive element Rp.

As has been explained with reference to the equations (1) and (2), the output voltage Vp is given as: Vp = K

Ip = C

then, from the equations (2) and (3), the following relationship is obtainable:

Vp = K

thus, if the relationship of the equation (3) is obtainable by means of the characteristic of the second controlling means t2, then the exact inverse proportion between the luminous intensity and the output voltage Vp is obtainable.

In order to attain the abovementioned characteristic, the second controlling means t2 should have the following characteristic between its input X and output Y:

Y = hX

where h is a constant. With the characteristic as abovementioned, the output Y of the second controlling means for an input voltage of Vp = KC

Y = hX

where K3 is a constant. Accordingly, the first controlling means t1 controls its output current Ip so as to be proportional to the output K3

The characteristic of the equation (3.2) is the theoretical characteristic, which is shown by a solid curve in the graph of FIG. 3. However, it has been difficult to attain such a characteristic by means of a simple circuit. However, in practical operation, the abovementioned characteristic can be approximated by the following characteristic if constants are properly selected:

Y = b + d

The dotted curve in FIG. 3 shows the curve of the function of the equation (3.4).

The abovementioned characteristic of the equation (3.4) can be realized by utilizing a logarithmic function of a diode or diodes.

A preferred fundamental example embodying the present invention is shown in FIG. 4, wherein details of the first and the second controlling means t1 and t2 are shown. In FIG. 4, the first controlling means comprises a first transistor T1, the collector of which is connected to one end of the photoconductive element Rp. The second controlling means t2 comprises a second transistor T2, the base and the emitter of which are connected across both ends of the photoconductive element Rp, and to the collector of which are connected a diode D and a variable resistor R2 in series. The junction point p between the collector of the second transistor T2 and the diode D is for logarithmic-conversion and is connected to the base of the first transistor T1.

In general, the voltage across both terminals of a diode or diodes in series connection is proportional to the logarithm of the current flowing through the diode, and accordingly, the voltage Vpq between the points p and q is given as

Vpq = R2

wherein d is a constant, and i is the current flowing through the diode D and the resistor R2.

Since the collector current Ip is proportional to the base input voltage Vpq of the transistor T1,

Ip = L

wherein L is a constant. The constants L and d should be properly selected by suitably selecting circuit constants, in order to attain good approximation between the theoretical Y = X

FIG. 5 shows a more practical embodiment provided with two variable resistors R2 and Rv as characteristic-approximation adjusting means. The apparatus also provides a pair of thermistors H1 and H2 for termperature compensation, a current adjusting transistor Q3 and a shunt resistor Bs. A Darlington connection consisting of a pair of transistors Q1 and Q2 is employed in place of the second transistor T2, in order that only very little input current to the base of the transistor Q1 is required. The transistor Q3 is provided connecting its collector, emitter and base to the positive end of the D.C. source, one end of the photoconductive element Rp, and a moving arm of the variable resistor Rv, respectively. As will be explained later, the variable resistor Rv is for adjusting the curve for good approximation in the high luminous intensity range, and the variable resistor R2 is for adjusting the curve for good approximation in the low luminous intensity range. Further, a series connection of several diodes may be employed in place of the diode D to ensure higher reverse breakdown voltage. In considering the operation, the circuit of FIG. 5 can be represented by the equivalent circuit of FIG. 6.

In FIG. 6 since both ends of the variable resistor Rv are connected across both ends of the D.C. source DCS, a divided voltage is applied to the movable contact of the variable resistor Rv and this voltage applied to the base of the transistor Q3. On account of the shunt resistor Rs, most of the emitter current of the transistor Q3 flows through the shunt resistor Rs, and accordingly, very little of the emitter current flows through the photoconductive element Rp. Accordingly, the emitter current of the transistor Q3 is little influenced by the change of the current Ip flowing through the photoconductive element Rp, ensuring a constant voltage Vo between the collector and the emitter of the transistor Q3. This voltage Vo is dependent only on the position of the moving contact of the variable resistor Rv.

The total of the abovementioned voltage Vo and the voltage Vp across the ends of the photoconductive element Rp is applied across the emitter and the base of the transistor T2, as illustrated in FIG. 6.

Now, defining the center value of the luminous intensity as Eo, the resistance and the current of the photoconductive element for this luminous intensity to be Rpo and Ipo, respectively, and the collector current of the transistor T2 and the voltage between points p and q for the abovementioned condition to be io and Vpqo, respectively, then the following relationships are given from the equations (1), (3) and (3.3):

Rpo = K

accordingly

K = ) Rpo/Eo

Ipo = C

accordingly

C = Ipo/Eo

By substituting the abovementioned K and C of the equations (4.1) and (4.2) into the equations (1) and (3), the following relationships are given:

Rp = K

ip = C

next, by defining i' as the collector current of the transistor T2 for the condition Vp = 0, on account of the linear characteristic between the base voltage Vo + Vp and collector current i of the transistor T2, the following relationship is given:

i = i' + K1

Also, from the equations (3.1) and (5.3),

i = i' + K1

wherein K2 = K1

(i - i')E = k2 (5.4)

and by applying the aforementioned condition of io for Eo in the equation (5.4),

(io - i') Eo = K2 (5.5)

from the equations (5.4) and (5.5),

i = i' + (io - i') (Eo/E) (6)

from the equations (4) and (6),

Ip = L {R2

for a small luminous intensity, the logarithmic term of the equation (8) is negligibly small, and accordingly, the condition i'<< (io - i) (Eo/E) is realized for a practical circuit condition. Therefore, we can express Ip as follows:

Ip ≉ L

since this equation (9) has the value R2 but excludes the value Rv, the adjustment for the proximation of the curve Y = b + dlog (X + γ) to the theoretical curve Y = X

For a large luminous intensity, the logarithmic term becomes predominent and therefore, we can express Ip, as follows:

Ip =⇋ + L

since this equation (10) does not have R2, the adjustment for the approximation can be made by adjusting only the variable resistor Rv. Namely, by adjusting the resistor Rv, the voltage Vo between the collector and the emitter of the transistor Q3 is varied, and the current i' in the equation (6) is also varied.

Thus, for both the ranges of large luminous intensity and small luminous intensity, the characteristic curve of the apparatus of FIG. 5 is well approximated to that of the theoretical curve.

From the equation (3) for the value Ipo and Eo,

Ipo = C

and from the equations (3) and (10.1),

Ip/Ipo = (E/Eo)

From the equation (3.1),

Vpo = K

and from the equations (3.1) and (10.3),

Vp/Vpo = (E/Eo)

In FIG. 7 the ordinate represents values of Ip/Ipo, and the abscissa represents values of E/Eo. The solid curve indicates the theoretical characteristic which is represented by the equations (3) and (3.1) wherein γ = 0.85, while the dotted curve indicates the experimental result of the circuit of FIG. 5. In the dotted curve, the curve in the left and right parts are adjusted by the variable resistors R2 and Rv, respectively. Thus, by adjusting the variable resistors R2 and Rv, the dotted line can be well approximated to the solid line.

The apparatus of the present invention has a low noise level for the following reason:

Possible noises produced in a circuit such as illustrated in FIG. 6 takes place at the bases of the transistors. Accordingly, we should consider the noises at the bases. A small part of the noise at the base of the transistor Q3 is applied to the base of the transistor T2, since most of the emitter current of the transistor Q3 flows in the shunt resistor Rs. The noise at the base of the transistor T2 produces the noise in the current i. From the equations (2) and (4) the following relationship is found:

Vp α R2

Namely, the output voltage Vp consists of a first part which is proportional to the current i and a second part which is a logarithmic compression of the current i. A noise, i.e., a small fluctuation in the current i, makes a resultant noise, i.e., a small fluctuation in the voltage Vp. Such a resultant noise consists of a first part originated from the first part R2