Input curve

Operating characteristics of transistors. i–v curves

Bipolar Junction Transistors (BJT) have 2 behavioral or operating characteristics:

- The input or transfer characteristics and

- Output characteristics.

These are relationships between certain currents and voltages (i-v characteristics) and can be graphically represented by the input or output curves of the device.

These characteristics are usually given in the Common Emitter configuration, in which the transistor is placed in such a way that its Emitter is the common terminal between the input (Base terminal) and the output (Collector terminal).

Input characteristics

The input or transfer characteristics of a transistor are given by the relationship between the Collector Current (iC) and the Base-Emitter Voltage (vBE), for a specific Collector-Emitter Voltage (VCE) value.

This iC - vBE relationship is defined by the Shockley diode equation:

Where Is is the Reverse Saturation Current.

This is the current that arises at the junction of the Base (crystal P) and the Emitter (crystal N) of the transistor, in this case of the NPN type, when it is reverse biased; that is, when the negative pole of the battery (-) is connected to the crystal P of the Base and the positive pole (+) of the battery to the crystal N of the Emitter. In this situation, the Base - Emitter "diode" should not let the current conduct; however, due to the temperature, a small current called Reverse Saturation Current (Is) will be produced, which can take a value between 10⁻¹⁸ and 10⁻⁹ Amps, depending on the device and its encapsulation.

In our case we are going to use the BC337 with a TO-92 type plastic encapsulation:

BC 337 with TO-92 type plastic encapsulation

We are going to assemble the following circuit with real components:

whose scheme in the simulator would be the following:

In it we are going to reverse bias the collector of the transistor by means of a VCC battery, whose positive pole we connect to the negative crystal of the transistor, the collector.

Likewise, we directly polarize the Base of the transistor by means of another VBB battery, whose positive pole we connect to the Positive crystal of the transistor, the Base.

Next we measure in the circuit with real components in operation values ​​of voltages and currents with a multimeter and we obtain the following values:

VBB = 3,76 v

IB = 37 𝛍A

V of RB = 3,14 v

VBE = 684 mv

VCC = 8,48 v

IC = 9 mA

V of RC = 7,27 v

VCE = 1,17 v

On the other hand, VT is the Thermal Voltage.

Indeed, the VT term of the equation is the Thermal Voltage, which at ambient temperature is 0.025v.

With all this, we can calculate Is if we substitute values ​​in the equation, giving us a value of 1.18 x 10⁻¹⁴ Amps.

Now we can graphically represent the Shockley equation, which corresponds to an exponential curve:

Gráfica obtenida en Geogebra

This relationship between the Collector Current (iC) and the Voltage at the Base-Emitter junction (vBE) is similar to the Current / Voltage relationship of diodes.

In the graph it can be seen that up to 0.5 or 0.6 v of vBE, iC is practically = 0. With higher values ​​we obtain an exponential increase in iC, in such a way that the values ​​of iC with which we normally work , will be between 0.6 v and 0.8 v of vBE. So for calculations, the value of VBE = 0.7 v is usually taken as a constant.

We can consult the technical data sheets ofthe BC337 with plastic encapsulation type TO-92.

In them you can find the following graphs that relate the Collector Current (iC) with the Base-Emitter Voltage (vBE) for a Collector-Emitter Voltage (VCE) of 1 v:

BC 337 IC - VBE relationship

Note that depending on the temperature, different iC-vBE curves are obtained. At ambient temperature of 25ºC (298 K), an IC of about 10mA corresponds to a VBE of about 0.635v.

Although for these conditions of temperature (25ºC / 298 K), IC (10 mA) and VCE (1 v), the value of VBE can be included in a range of values, which can vary from 0.510 v to 0.800 v, as indicated these other manufacturers in their technical data sheets:

Range of values ​​in the IC - VBE relationship of the BC 337 at 25ºC (298 K)

We can check how our VBE value (684 mv) obtained with the multimeter is within the limit values ​​of the graph.

iB - vBE relationship

But in this post we are going to take the input characteristics of the transistor as the relationship between the Base Current (iB) and the Base-Emitter Junction Voltage (vBE), instead of the relationship between the Collector Current (iC) and the Voltage at the Base-Emitter (vBE) junction as we have done so far.

To determine them we are going to use the simulator.

Let's design the following circuit:

In the Base mesh we are going to insert a battery that matches the 684 mv of VBE obtained with the multimeter in the real components circuit and we will do the same in the Collector mesh; we will insert a 1.17v battery of VCE obtained in the real circuit.

If we measure the Base current (IB), we have a value almost twice that obtained in the real circuit (69.8 𝛍A).

We will have to modify the parameters of the BC 337 transistor of the simulated circuit so that its functioning is as similar as possible to that of the real circuit.

If we double "click" on the BC 337 transistor in the simulator circuit, the following window opens:

If we select the "Edit model" button, we will access the values ​​of the different design parameters of the transistor:

 

In order for the BC 337 to work as close as possible to the transistor that we have used in the circuit of real components, we will have to change the value of the Gain that comes by default. To do this we will select the BF (Ideal maximum forward beta) box and instead of 175, we will choose the "Use default" option, staying at a value of 100.

In addition, we will also change the value of the Reverse Saturation Current (IS). And instead of the value that marks us, we will introduce the value obtained at the beginning of this publication (1.18 x 10⁻¹⁴ Amps).

Once these values ​​have been modified, we will "click" the "Change component" button so that the new values ​​are saved.

When we accept we return to the designed circuit, but the transistor appears marked with an asterisk:

If we now run the circuit in the simulator, we will get an IB more similar to that of our real component circuit (40.301 𝛍A).

Now we can determine the iB - vBE curves in the simulator.

On this circuit with the modified transistor, we will perform a sweep analysis ("DC sweep") including both DC sources. To do this, in "Simulate" we choose "Analysis" and "DC sweep". In "Source 1" we select the "VBE" source and give it the values ​​from 0 to 3 v taken in increments of 0.01 v. After enabling the use of a second source, we choose "VCE", giving it only 3 values: 5, 10 and 15 v.

In "Output" we select the variable "ib" and we give it to simulate:

We obtain 3 curves, one for each "VCE", with very high values ​​of Base Current (iB). On the order of hundreds of mA:

BC 337 input curves obtained in the simulator

Observe how for higher values ​​of VCE the curve shifts to the right. But this effect is only visible at very high values ​​of iB (on the order of hundreds of milliamps).

For more normal and much smaller values ​​of iB, of the order of a few tens of 𝛍As, a single curve can be considered, in which we can again observe that the values ​​of iB, with which we normally work, will be between the 0.6v and 0.8v of vBE

To finish, we can translate the values ​​of VBE and IB of the circuits to the input curve of the transistor:

Summarizing.

In this publication, the input characteristics of bipolar transistors, of the BC 337 in particular, have been introduced; which are given by the Shockley equation, whose graphic representation is an exponential curve that relates the Collector Current (iC) with the Voltage between the Base and the Emitter (vBE). We have seen that in this curve the value of VBE is close to 0.7 v. A circuit has been built with real components and voltage and current values ​​have been measured with the multimeter in order to determine the value of the Reverse Saturation Current (Is) and thus be able to represent said input curve.

We have then analyzed this curve in the technical data sheets supplied by different manufacturers for the BC 337 transistor with TO-92 type plastic encapsulation.

Subsequently, the relationship between the Base Current (iB) and the Voltage between the Base and the Emitter (vBE) has been defined as the input characteristic of bipolar transistors. Said characteristic is given by another exponential curve that is the one that is usually used in textbooks and publications that deal with the study of bipolar transistors.

To do this, a circuit has been designed in the simulator in which a BC 337 device modified in its Current Gain for direct current and its Reverse Saturation Current has been inserted, with the intention of making its operation resemble as much as possible the of the circuit device designed with real components.

A "sweep" analysis has been carried out in the simulator and the input curve that relates iB to vBE has been obtained, effectively indicating that the simulator circuit transistor operates very similarly to that of the circuit device with real components.

Finally, the operating point of both transistors (virtual and real) in said curve has been indicated.

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