Working Principle of Thermistor

Thermistor have a Negative Temperature Coefficient (NTC) i.e. resistance decreases as the temperature increases. The materials used in the manufacture of thermistors include oxides of cobalt, nickel, copper, iron, uranium and manganese. The thermistor has very high temperature coefficient of resistance of the order of 3 to 5% per ºC. The resistance at any temperature T is given by,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\beta \text{ }\left( \frac{1}{T}-\frac{1}{{{T}_{0}}} \right)\]

Where,

R_T – Thermistor resistance at temperature T (K)

R₀ – Thermistor resistance at temperature T₀ (K)

β – A constant determined by calibration

At high temperature, equation (1) reduces to,

\[{{R}_{T}}={{R}_{0}}\text{ exp }\left( \frac{\beta }{T} \right)\]

Working & Symbol of Thermistor

Figure 1.

The resistance-temperature characteristics is shown in Fig. 1 (b) and symbol in Fig. 1 (a). The curve is non-linear and the drop in resistance from 500Ω to 100Ω occurs for an increase in temperatures from 20 to 100ºC. The temperature of the device can be changed internally or externally. An increase in current through the device will raise its temperature carrying a drop in its terminal resistance. Any externally applied heat source will result in an increase in its body temperature and drop in resistance. This action tends itself well to control mechanisms.

Types of Thermistor

Figure 2: Various configurations of thermistor.

The thermistors are available in various configurations such as beads, disc, rod, washer as shown in Fig. 2. The smallest thermistors are made in the form of beads. Some are as small as 0.15 mm in diameter. And where greater power dissipation is required, thermistors obtained are in disc, washer or rod forms.

Advantages of Thermistor

1. Small size and low cost.
2. Fast response over narrow temperature range.
3. Good sensitivity in the NTC region.

Disadvantages of Thermistor

1. Non-linearity in resistance versus temperature characteristics.
2. Unsuitable for wide temperature range.
3. Very low excitation current to avoid self-heating.
4. Need of shielded power lines, filters etc. due to high resistance.

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When the anode terminal of a diode is connected to the negative terminal of voltage source and cathode to the positive terminal then the diode is reverse biased as shown in Fig. 1 (a) and its symbolic representation in Fig. 1 (b).

Operation of Reverse Biased PN Junction Diode

Figure 2: Reverse biased effect on layer and barrier voltage.

When an external bias is applied to a diode, positive to cathode and negative to anode, electrons from N-side are attracted to the positive terminal and holes from P-side are attracted to the negative terminal. As shown in Fig. 2, holes on P-side of junction are moved away from the junction and electrons are also moved away from the junction on N-side. This results in the depletion region to be widened and the barrier voltage to be increased.

As the barrier voltage at the junction increases, the holes and electrons are not able to cross the junction, hence the majority charge carrier current will be zero and the junction is said to be reverse biased. There will be very small reverse current due to minority charge carrier. Because of this very small reverse current flow, a reverse biased PN junction diode offers very high resistance. As there is no possibility of majority charge carriers the current flowing across a reverse biased junction, minority carriers i.e. holes on N-side and electrons on P-side, generated on each side can cross the reverse junction. The electrons on the P-side are attracted to the positive voltage crossing the junction on the N-side. The holes from N-side flow across to the negative voltage on P-side. Due to this, small current flows through the junction. Only a very small reverse bias voltage is necessary to move all available minority carriers across the junction and if voltage bias is increased further, current will not increase. And hence this current is referred as reverse saturation current. The reverse saturation current is very small ranging from nanoamperes to microamperes. It depends on the junction area, temperature and semiconductor material.

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Figure 1.

When anode is connected to the positive terminal of a battery/voltage source and cathode to the negative terminal, then the diode is said to be forward biased as shown in Fig. 1 (a) and its symbolic representation is shown in Fig. 1 (b).

Operation of Forward Biased PN Junction Diode

Figure 2: Forward biased effect on layer and barrier voltage.

When PN junction is forward biased, the holes (being positively charged) are repelled by the positive terminal of voltage source and forced to move towards the junction. Similarly, the electrons (negatively charged) are repelled by the negative terminal of voltage source and move towards the junction. As they get some energy from the voltage source, some of the holes and electrons enter the depletion layer and recombine themselves. This results in reduction in width of depletion layer and the barrier potential with forward bias as shown in Fig. 2. Therefore, it causes a large current to flow through the diode. When the applied bias voltage is increased from zero, the barrier voltage gets decrease until it effectively disappears and majority charge carriers easily flow across the junction. The electrons from N-side are now attracted across to the positive bias terminal on P-side and holes from the P-side flow across to the negative terminal on the N-side. Thus, a majority carrier current flows and the junction is said to be forward biased. This large current due to majority charged carrier in forward biased is called as forward current.

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Figure 1: V-I Characteristics of a PN Junction Diode.

VI Characteristics of pn junction diode, is a graph between the voltage applied across the terminals of a device and the current that flows through it. Fig. 1 shows the V-I characteristics of a typical PN junction diode with respect to breakdown voltage (V_BR). The complete V-I characteristics is divided into two parts, namely forward characteristic and reverse characteristic.

Forward characteristics :

Figure 2.

Fig. 2 (a) shows the circuit arrangement for obtaining forward characteristic of a diode. In this circuit, the diode is connected to a d.c. voltage (V_AA) through the potentiometer (P) and a resistance (R). The potentiometer helps in varying the voltage applied across the diode. The resistance (R) is included in the circuit, so as to limit the current through the diode. A voltmeter is connected across the diode to measure the voltage and milliammeter to measure the current in the circuit. The positive terminal of the voltage source is connected to the anode and the negative terminal to the cathode, hence the diode is worked in forward-biased condition. Increase the voltage and record the corresponding values of diode current. The graph between applied voltage and current is plotted as shown in Fig. 2 (b).

Forward characteristics show that no current flow till the point P is reached. It is due to the fact that, applied voltage is less than the junction voltage i.e. 0.7 V for Silicon and 0.3 V for Germanium. As the voltage is increased above point P, the diode current increases rapidly. The voltage at which the diode starts conducting is called a knee voltage, cut-in voltage or threshold voltage. The knee voltage is denoted by V_R or V_γ. Its value is 0.6 V for Si and 0.2 V for Ge.

Reverse characteristics :

The circuit arrangement for obtaining reverse characteristics of a diode is shown in Fig. 3 (a). In the circuit a diode is connected in reverse biased condition i.e. cathode is connected to the positive terminal of voltage source and anode to the negative terminal. The applied reverse voltage is gradually increased above zero and the values of diode current are measured. The graph plotted between reverse voltage and current is shown in Fig. 3 (b). The curve OCD is called reverse characteristics of a diode. The reverse characteristics indicate that when applied reverse voltage is less than breakdown voltage (V_BR), the diode current is small and remains constant. This current is called as reverse saturation current (I_o).

When reverse voltage is increased to a large value, the diode reverse current increases as rapidly as shown by curve CD in Fig. 3. The applied reverse voltage at which large current flows through the diode is known as breakdown (V_BR) voltage of a diode.

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Working Principle of Strain Gauge

Their working principle is based on piezo-resistive effect. The piezo-resistive effect states that if a metal conductor is stretched or compressed, its length and diameter changes. Therefore its resistance also gets changed. Similarly the resistance of a metal conductor changes when it is strained.

Fig. 1 shows an unstrained wire of elastic material with length L, Diameter: D and Area of cross-section = A.

\[R=\rho \frac{L}{A}=\rho \frac{L}{(\pi /4){{D}^{2}}}\]

\[R=\rho \frac{L}{A}=\rho \frac{L}{\left( \frac{\pi }{4} \right){{D}^{2}}}\]

Where,

ρ = Resistivity of the wire in Ω – m

If this wire of elastic material (Strain Gauge) is subjected to tension, its length increases and diameter reduces. These changes in the dimensions due to applied force are shown in Fig. 2.

Let the change in length = ΔL and change in diameter = ΔD. To find the change in resistance (ΔR) due to applied force we use Poisson’s ratio.

\[\text{Using Poisson ratio (}\mu \text{) = }\frac{(\Delta D/D)}{(\Delta L/L)}\]

But,

\[\frac{\Delta L}{L}=\sigma =\text{ Strain}\]

Therefore,

\[\Delta D=\mu .\sigma .D\]

Thus the change in resistance is given by ΔR = Rσ (1+2µ).

From the above equation, we can conclude that the resistance of the wire increases due the applied force. The gauge factor (G) of a strain gauge is defined as the unit change in resistance per unit change in length. Therefore,

\[G\text{= }\frac{(\Delta R/R)}{(\Delta L/L)}\] (Ranges from 1.5 to 1.7)

Types of Strain Gauge

The two types of strain gauges as

1. Bonded Strain Gauge
2. Unbonded Strain Gauge

Bonded Strain Gauge

Fig. 3: Bonded Type Strain Gauge.

A bonded strain gauge consists of a grid of fine wire which is fixed on a base of a thin paper sheet as shown in Fig. 3. The paper sheet is bonded with an adhesive to the spot under measurement. When force is applied to the surface, to which the strain gauge is bonded, the resistance of the grid wire changes due to the change in length and diameter of the wire. This change in the resistance can be measured by connecting the strain gauge in one of the arms of the Wheatstone bridge that generates equivalent voltage. The bonded strain gauge is useful only for measuring very small displacements. To measure large displacements, the strain gauge is bonded to a flexible element like cantilever beam. The displacement can then be measured at the end of the cantilever beam.

Unbonded Strain Gauge

Fig. 4: Unbonded Type Strain Gauge.

As shown in Fig. 4, an unbonded strain gauge is constructed by fitting the gauge wire on a stationary frame having a movable armature fixed at the centre. The armature can be moved only in one direction and its travel is limited by four strain gauge wires. If an external force is applied to the strain gauge or the armature is moved, the gauge wire gets stretched showing a proportional change in its resistance value which can be measured with the Wheatstone bridge. The output voltage of the Wheatstone bridge can be calibrated according to displacement of the armature.

Advantages of Strain Gauge

1. High accuracy and reliability.
2. Small size and easy to use.

Disadvantages of Strain Gauge

1. High cost.
2. The changes in temperature may affect the output.

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Types of Summing Amplifier (Adder) Using Op-Amp

Depending on the polarity or sign of the output voltage the adder circuits can be classified into two categories as :

1. Inverting adder and
2. Non-inverting adder.

Inverting Adder or Inverting Summing Amplifier

Figure 1: Summing Amplifier.

Fig. 1 shows the “inverting summing amplifier” configuration with three inputs V₁, V_2, and V₃. Depending on the relation between the feedback resistor R_F and the three input resistances R₁, R_2, and R₃ we can use the same circuit shown in Fig. 1 as a summing amplifier, scaling amplifier or averaging amplifier. V₁, V₂ and V₃ are three input signals applied simultaneously to the inverting terminal of the OP-AMP through resistors R₁, R₂ and R₃ respectively. V₁, V_2, and V₃ are measured with respect to ground. R_F is the feedback resistor, connected between the output terminal and the inverting input terminal of OP-AMP. The non-inverting input terminal is connected to ground. So the configuration of Fig. 1 is basically an inverting amplifier with three inputs. Let the currents through the resistors R₁, R₂ and R₃ be I₁, I₂ and I₃ respectively. For the analysis of this circuit, we assume that the OP-AMP is ideal. Hence its input resistance is R_i = ∞. Therefore the currents I_B1 and I_B2 are zero. In addition to this, Node A is at virtual ground potential.

Expression for the output voltage :

Apply KCL at node A of Fig. 1 to write,

\[{{I}_{1}}+{{I}_{2}}+{{I}_{3}}={{I}_{B2}}+{{I}_{F}}\]

But as R_i of the OP-AMP is ideally infinite, I_B2 = 0, and V_A = V_B = 0 due to virtual ground concept.

Hence,

\[{{I}_{1}}+{{I}_{2}}+{{I}_{3}}={{I}_{F}}\]

On the input side,

\[{{I}_{1}}=\frac{{{V}_{1}}-{{V}_{A}}}{{{R}_{1}}}=\frac{{{V}_{1}}}{{{R}_{1}}}\text{ as }{{V}_{A}}=0\]

Similarly,

\[{{I}_{2}}=\frac{{{V}_{2}}-{{V}_{A}}}{{{R}_{2}}}=\frac{{{V}_{2}}}{{{R}_{2}}}\]

\[{{I}_{3}}=\frac{{{V}_{3}}-{{V}_{A}}}{{{R}_{3}}}=\frac{{{V}_{o}}}{-{{R}_{3}}}\]

And on the output side,

\[{{I}_{F}}=\frac{{{V}_{A}}-{{V}_{o}}}{{{R}_{F}}}=-\frac{{{V}_{o}}}{-{{R}_{F}}}….(1)\]

Substituting these values in Equation (1) we get,

\[\frac{{{V}_{1}}}{{{R}_{1}}}+\frac{{{V}_{2}}}{{{R}_{2}}}+\frac{{{V}_{3}}}{{{R}_{3}}}=-\frac{{{V}_{o}}}{{{R}_{F}}}\]

Or,

\[{{V}_{o}}=-\left[ \frac{{{R}_{F}}}{{{R}_{1}}}{{V}_{1}}+\frac{{{R}_{F}}}{{{R}_{2}}}{{V}_{2}}+\frac{{{R}_{F}}}{{{R}_{3}}}{{V}_{3}} \right]\]

In Equation (1) if we substitute R_F = R₁ = R₂ = R₃ = R then we get,

\[{{V}_{o}}=-({{V}_{1}}+{{V}_{2}}+{{V}_{3}})\]

Thus output voltage is the negative sum of the input voltage. Therefore this circuit is called as “Inverting adder” or “Inverting summing amplifier”. Similarly, we can add any number of inputs.

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Figure 1: Voltage Follower (Buffer) Circuit Diagram.

Figure 2: Waveforms of Voltage Follower (Buffer).

Circuit diagram of Voltage Follower (Buffer) Using Op-Amp

When R₁ = ∞ and R_F = 0 the non-inverting amplifier gets converted into a voltage follower or unity gain amplifier. When the non-inverting amplifier is configured so as to obtain a gain of 1, it is called as a voltage follower or unity gain non-inverting buffer. The schematic diagram for a voltage follower is as shown in Fig. 1. The voltage follower configuration of Fig. 1 is obtained by short circuiting R_F and open circuiting R₁ connected in the usual non-inverting amplifier configuration of Fig. 1. Thus all the output voltage is fed back to the inverting input of the OP-AMP. Therefore the feedback factor of this circuit i.e. B = 1.

Closed Loop Voltage Gain (A_VF) of Voltage Follower (Buffer) Using Op-Amp

Consider the expression for the closed loop gain of a non-inverting amplifier, that is,

\[{{A}_{VF}}=1+\frac{{{R}_{F}}}{{{R}_{1}}}….(1)\]

In above equation 1, substitute the values of R_F = 0 and R₁ = ∞ to get the closed loop gain of the voltage follower as,

\[{{A}_{VF}}=1\]

Therefore the output voltage will be equal to and in phase with the input voltage, as shown in Fig. 2. Thus voltage follower is a non-inverting amplifier with a voltage gain of unity.

Why Voltage Follower is called a buffer?

A buffer is an electronic circuit that isolates the input from the output, providing either no voltage or a voltage that is the same as the input voltage. It has a voltage gain of unity (1). A voltage buffer must have a very high input impedance and very low output impedance so that it draws a very small current from input and can supply. Since a voltage follower circuit satisfies all these requirements, it is called as a buffer.

Applications of Voltage Follower (Buffer) Using Op-Amp

1. As a buffer amplifier so as to avoid the loading of the source.
2. It is used as the output stage because of its low R_o.
3. It can be used for impedance matching.

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Figure 1: Inverting Amplifier.

Circuit diagram of Inverting Amplifier Using Op-Amp

The circuit diagram of an inverting amplifier is as shown in Fig. 1. The signal which is to be amplified is applied at the inverting (-) input terminal of the OP-AMP.

Working and Waveforms of Inverting Amplifier Using Op-Amp

The signal to be amplified (V_s) has been connected to the inverting terminal via the resistance R₁. The other resistor R_F, connected between the output and inverting input terminals is called as the feedback resistance. It introduces a negative feedback. The non-inverting (+) input terminal is connected to ground. As the OP-AMP is an ideal one, its open loop voltage gain A_v = ∞ and input resistance R_i = ∞. The negative sign for A_v is due to the inverting configuration. The input and output voltage waveforms are as shown in Fig. 2. Output is an amplified and inverted version of the input signal V_S.

Closed Loop Voltage Gain (AVF) of Inverting Amplifier Using Op-Amp

Looking at Fig. 1 we can write that,

\[{{V}_{o}}=\left| {{A}_{v}} \right|\times {{V}_{d}}\]

\[{{V}_{d}}=\frac{{{V}_{o}}}{\left| {{A}_{v}} \right|}\]

Where,

A_v = Open loop gain of OP-AMP.

As we know an open loop gain of OP-AMP is ∞.

\[{{V}_{d}}=\frac{{{V}_{o}}}{\infty }=0\]

But,

\[{{V}_{d}}={{V}_{1}}-{{V}_{2}}\]

\[{{V}_{1}}-{{V}_{2}}=0….(1)\]

As the non-inverting (+) input terminal is connected to ground, V₁ = 0. Substituting this value in Equation (1) we get,

\[{{V}_{2}}=0\]

Thus V₂ is at ground potential. Since the input resistance R_i = ∞, the current going into the OP-AMP will be zero. Therefore the current “I” that passes through R₁ will also pass through R_F as shown in Fig. 1. As the input voltage V_S is being measured with respect to ground and as V₂ is at ground potential we can say that the input voltage V₂ is voltage across R₁ and voltage across R_F is output voltage. The input voltage, V_S is given by,

\[{{V}_{S}}=I\text{ }{{R}_{1}}….(2)\]

And the output voltage Vo is given by,

\[{{V}_{o}}=-I\text{ }{{R}_{F}}….(3)\]

We can write Equations (2) and (3) because V₂ is at approximately ground potential (virtual ground).

\[\text{Closed loop gain, }{{A}_{VF}}=\frac{{{V}_{o}}}{{{V}_{S}}}\]

Substituting the expression for V_o and V_S we get,

\[{{A}_{VF}}=-\frac{I{{R}_{F}}}{I{{R}_{1}}}=-\frac{{{R}_{F}}}{{{R}_{1}}}….(4)\]

And,

\[{{V}_{o}}={{A}_{VF}}\times {{V}_{S}}\]

Conclusions from the expression for A_VF :

From Equation (4) we can draw the following important conclusions :

1. The value of closed loop voltage gain A_VF does not depend on the value of open loop voltage gain A_v.
2. Value of A_VF can be very easily adjusted by adjusting the values of the resistors R_F and R_i. Generally the feedback resistor R_F is a potentiometer to adjust the gain to its desired value.
3. The output is an amplified inverted version of input.

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UJT is an acronym for Unijunction Transistor. The basic structure of a unijunction transistor is as shown in figure (1). It contains a lightly doped N-type silicon bar on which a small portion of heavily doped P-type material is alloyed. The P-type material doped into the N-type bar forms a single P-N junction. Because of this, it is known as unijunction. The N-type bar has two ohmic contacts at its ends named as base-1(B₁) and base-2(B₂) and the ohmic contact coming out of P-region is named as emitter (E). The emitter junction is created (or produced) closer to base-2 (B₂) than base-1(B₁), so the device is not symmetrical. The symbol for the transistor is shown in figure (2). The emitter leg is drawn at an angle to the vertical line representing the N-type material slab and the arrowhead indicates the direction of conventional current flow when the transistor is operating in the active region.

The basic UJT circuit includes a diode and two base resistances R_B1 and R_B2, in which R_B1 is a variable resistor. The value of R_B1 varies between 5 kΩ and 50 Ω with the change in emitter current from 0 µA to 50 µA.

VI Characteristics of Unijunction Transistor (UJT)

Figure 3: VI Characteristics of Unijunction Transistor (UJT).

The forward and reverse operating conditions or ON and OFF states of UJT depends on the emitter voltage V_E,

(i) If the voltage at emitter terminal V_E is not sufficient to turn ON the diode, it acts as an open switch and small leakage current I_E0 flows through the circuit. In this case, the transistor operates is in cut-off region and emitter current I_E = 0.

The resistance between the terminals B₁ and B₂ for I_E = 0 is given by,

\[{{R}_{BB}}={{R}_{B1}}+{{R}_{B2}},{{I}_{E}}=0\]

Here,

R_BB — Interbase resistance

Using voltage-divider rule, the potential drop across R_B1 is determined as,

\[{{V}_{{{R}_{B1}}}}=\frac{{{R}_{B1}}}{{{R}_{B1}}+{{R}_{B2}}}{{V}_{BB}}\]

\[=\frac{{{R}_{B1}}}{{{R}_{BB}}}{{V}_{BB}}\]

\[=\eta {{V}_{BB}}\]

Where,

η — Intrinsic stand-off ratio

\[\eta =\frac{{{R}_{B1}}}{{{R}_{B1}}+{{R}_{B2}}}=\frac{{{R}_{B1}}}{{{R}_{BB}}}\]

(ii) The emitter voltage, V_E reaches to peak point, when the voltage applied is greater than ηV_BB + V_B (V_B is the diode cut-in voltage). At this point, the UJT tum ON i.e., conducts and I_E increases. But, the voltage V_E reduces due to negative resistance characteristics.

(iii) When emitter voltage, V_E from peak point reaches valley point, V_V the transistor enters into saturation region.

The characteristics of UJT are plotted as shown in figure (3). From figure (3), it can be observed that, in negative resistance region or active region the voltage V_E reduces with increase in current I_E. In this region, when UJT starts conducting, the holes from P-type material are injected into N-type silicon bar. During this, the number of free electrons increases in N-type slab due to increased hole concentration, high conductivity takes place in transistor. Thus, the UJT exhibits negative resistance characteristics i.e., resistance decreases with increase in conductivity.

Applications of Unijunction Transistor (UJT)

1. UJT is used as a relaxation oscillator to generate sinusoidal waveforms.
2. It is widely used as sawtooth generator, sweep oscillator, and voltage detector.
3. Magnetic flux can be measured using UJT.
4. It is used in phase controllers and timing circuits.
5. In SCRs and Triac, UJT is used as a triggering circuit.

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The phototransistor is an optoelectronic device that generates or detects the signals from light incident on it. The symbol of phototransistor is shown in figure (1).

The structure of a NPN bipolar phototransistor is illustrated in figure (2). The phototransistor is basically operated in an open-base configuration.

Figure 3: Diagram of an open-base phototransistor.

The schematic representation of open-base phototransistors is depicted in figure (3). From figure (3), it can be observed that the width of depletion region or junction between base and collector is large. When the base-collector junction is in reverse bias, the charge carriers emit out of the region and generates a photocurrent, I_L If the base-emitter junction is forward biased, the photo-transistor operates as a basic semiconductor BJT. From figure (3), the total current coming out from the emitter terminal is given by,

\[{{I}_{E}}=\alpha {{I}_{E}}+{{I}_{L}}\]

Here,

α – Current gain CB configuration.

As the base is open-circuited I_B = 0, which implies,

\[{{I}_{E}}={{I}_{C}}\] \[{{I}_{C}}=\alpha {{I}_{C}}+{{I}_{L}}\]

\[{{I}_{C}}(1-\alpha )={{I}_{L}}\] \[{{I}_{C}}=\frac{{{I}_{L}}}{1-\alpha }\]

Since,

\[\beta =\frac{\alpha }{1-\alpha }\text{ and }\alpha =\frac{\beta }{1+\beta }\]

\[\frac{\beta }{\alpha }=1+\beta \]

\[1+\beta =\frac{1}{1-\alpha }\]

\[{{I}_{C}}=(1+\beta ){{I}_{L}}\]

The factor (l + β) indicates the amount of amplification of I_L in a phototransistor. The frequency response of a phototransistor having a large Base-Collector junction area is limited by a capacitor. It can also be reduced using the Miller effect.

Applications of Phototransistor

1. In optocouplers, it is used as light detector.
2. It is used in punch card readers.
3. In digital logic circuits.
4. It is used in traffic light controllers, level indication devices, etc.
5. In SCR triggering circuits at low light levels.

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