How to calculate forward resistance of diode

Lab 1: Diode Characteristics

PURPOSE:

The purpose of this experiment is to acquaint the student with the operation of semiconductor diodes. You will use a curve tracer to obtain the current-voltage (I-V) characteristics of a silicon diode. From these characteristics, you will determine several diode parameters including the dynamic resistance, rf = rd; the diode forward resistance, RF = RD; the cut-in voltage, Vγ; the forward diode ideality factor, n; and the breakdown voltage, VBR. All of these terms are defined below. You will find that most of these parameters depend on the current at which that parameter is measured. You will also compare the dc operation of a diode in a circuit with both the calculated and simulated operation.

PRE-LAB:

Review the INTRODUCTION section below. Simulate the diode characteristic using PSpice for comparison with experimentally measured results. Determine rd, Vγ, and n for the 1N4004 diode in your diode characteristic plot. Simulate the circuit shown in Figure 5 for the resistor (R) values shown using a DC sweep test (sweep Vin and R simultaneously; see Part 2 of previous lab for help).

EQUIPMENT:

For this laboratory session you will need the following:

a. Silicon diodes: 1 – 1N4004 diode or equivalent 1N4001 1 – 1N4744 diode These diodes are all silicon diodes with different breakdown voltages and different power handling capabilities. The 1N4744 is a Zener Diode and has the lowest breakdown voltage. It should be used when attempting to obtain the reverse breakdown voltage. The 1N4004 diode will be used extensively in circuits in other experiments.

b. Tektronix Type 571 curve tracer c. Breadboard d. Resistor decade box e. A computer with PSpice

INTRODUCTION:

Diode Structure

Figure 1

Figure 1 shows the physical and schematic circuit symbol of the diode. The band on the diode and the bar on the left of the circuit symbol represent the cathode (n-type material) and must be noted. The p-type material (the anode) in the diode is located to the right. The circuit symbol of the diode is an arrow showing forward bias, when the p-side is positive with respect to the n-side, and the direction of the arrow represents the direction of large current flow.

Ideal Diode Equation

The relationship between the diode current and voltage is given by the diode equation

:

 

  

 −= 1T

D nV

V

SD eII (1)

The terms in Equation (1) are defined as follows:

ID = the diode current (amperes).

VD = the voltage across the diode (volts).

IS = the reverse saturation current or the reverse leakage current (amperes).

IS is a function of the diode material, the doping densities on the p-side and n-side of the diode, the geometry of the diode, the applied voltage, and temperature. IS is usually of the order of 1 μA to 1 mA for a germanium diode at room temperature and of the order of 1 pA = 10

-12 A for a silicon diode at room

temperature. IS increases as the temperature rises.

VT = k T / q = the thermal equivalent voltage = 0.0258 V at room temperature

where

q = 1.6 x 10 -19

Coulombs = the electric charge,

k = 1.38 x 10 -23

J/K = Boltzmann's constant,

T = absolute temperature (Kelvin) [room temperature = 300 K], and

n = the ideality factor or the emission coefficient.

The Ideality Factor (n):

The ideality factor, n, depends on the type of semiconductor material used in the diode, the manufacturing process, the forward voltage, and the temperature. Its value generally varies between 1 and 2. For voltages less than about 0.5 V, n ~ 2; for higher voltages, n ~ 1. (Based on experimental measurements, at higher voltages, typically 1.15 ≤ n ≤ 1.2.)

The ideality factor, n, can readily be found by plotting the diode forward current on a logarithmic axis versus the diode voltage on a linear axis.

Equation (1) indicates that an increase in current ID by a factor of 10 represents an increase in exp(VD / n VT) by a factor of 10, as long as exp(VD / n VT) >> 1. If ΔVD is the change in voltage required to produce a factor-of-10 change in the current, then

( )

( ) mV3.590593.0V0258.030.230.2

30.210ln

⋅====∆

== ∆

nnnVnV Vn V

TD

T

D

And so,

mV60mV3.59

DD VVn ∆≈∆= (1)

To find n, it is only necessary to find the amount of voltage needed to increase the diode current by a factor of 10 and use Equation (1).

Figure 2: Graphs of the same forward diode current ID vs diode voltage VD as

(a) Linear plot and (b) Semi-log plot

Figure 2 shows example graphs of the forward diode current ID versus diode voltage VD as (a) Linear plot and (b) Semi-log plot. To calculate the ideality factor n, create the semi-log plot for the diode’s data. Draw a straight line through adjacent points, then read off coordinates where the current ID increases by powers of 10 (e.g., 0.0001, 0.001, 0.01, 0.1, …), as illustrated in Figure 2. Calculate ΔVD, the amount of voltage needed to increase the diode current by a factor of 10, and then divide by 59.3mV (or 60 mV) to calculate n:

147.1 0593.0

683.0751.0 =

− =n (2)

(Advanced note: The ideality factor is a measure of how close the diode matches “ideal” behavior. If the ideality factor is different from 1, it indicates either that there are unusual recombination mechanisms taking place within the diode or that the recombination is changing in magnitude. Thus, the ideality factor is a powerful tool for examining the recombination in a device.)

Cut-in Voltage Vγ:

A sketch of a diode characteristic, as it would be measured on a curve tracer, is shown in Figure 3. The curve tracer only measures the forward I-V or the reverse I-V characteristic in any one sweep. The characteristics shown in Figure 4 are the combination of the forward and reverse characteristics. Appreciable conduction occurs from around 0.4V to 0.7V for silicon and from around 0.2V to 0.4V for germanium at room temperature. The value of Vγ is a function of the current at which Vγ is measured. This point is discussed below and is one of the concepts you should master from this experiment. If the applied voltage exceeds Vγ, the diode current increases rapidly.

Figure 3: Diode forward I-V characteristic showing the definition of Vγ

The complete diode characteristic is shown in Figure 4, piecing together the forward-biased data and the reverse-biased data. Note that the scales of +V and –V may differ by a factor of 100, and while +I may be mA or A, –I is likely to be µA or nA.

Figure 4: Forward and reverse diode I-V characteristics

Diode Current and Diode Saturation Current:

If the diode is operated in the forward-bias region at room temperature (27 o

C = 300 K), the exponential first term in the brackets in Equation (1) dominates and the diode current equation is given approximately by

T D

nV V

SD eII = (3)

The current for forward bias is an exponential function of the applied voltage, VD.

If the diode is reverse-biased, only the small reverse current (the reverse saturation current or the reverse leakage current), −IS, flows. This current flows as long as the applied reverse voltage does not exceed the diode breakdown voltage, VBR. If the reverse voltage exceeds VBR, a large amount of current flows and the diode may be destroyed if there is not enough series resistance to limit the diode current. In silicon diodes, IS may be very small and VBR may be very large. Both of these values may be immeasurable on the curve tracers for diodes like the 1N4004.

Diode Resistance Three diode resistances are commonly calculated:

• DC or Static forward resistance, RF or RD

• AC or Dynamic forward resistance, rf or rd

• Reverse resistance, rr

Another diode resistance, RS, is also mentioned. RS refers to the sum of the diode's contact resistance, lead resistance, and internal diode resistance. It appears in PSpice simulations.

DC or Static forward resistance, RF or RD, is the total voltage drop across the diode divided by the current flowing through the diode, just as one would calculate using Ohm's Law. It includes contact resistance, lead resistance, material resistance, and the resistance of the p and n regions of the diode.

D

D F I

VR =

AC or Dynamic forward resistance, rf or rd: In practice we don't often use the static forward resistance; more important is the dynamic or AC resistance, which is the opposition offered by the diode to changing current. It is calculated by the ratio [change in voltage across the diode] / [the resulting change in current through diode] at the operating voltage, VD. That is, rd is the reciprocal of the slope of diode current versus voltage at the operating point.

currentin change resulting

in voltage change =

∆ ∆

=≡ D

D df I

Vrr

Applying the diode equation and differentiating, we find the dynamic forward resistance is given by

D

T

D

D d I

Vn dI dVr == (4)

Owing to the nonlinear shape of the forward characteristic, the value of AC resistance of a diode is in the range of 1 to 25 ohms. Usually it is smaller than DC resistance of the diode.

Reverse Resistance, rr: When a diode is reverse biased, besides forward resistance, it also possesses another resistance known as reverse resistance. It can be either DC or AC depending upon whether the reverse bias is direct or alternating voltage. Ideally, the reverse resistance of the diode is infinite. However, in actual practice, the reverse resistance is never infinite, due to the existence of leakage current in a reverse-biased diode.

The reverse resistance, rr, is given by the reciprocal of the slope of the reverse characteristic, prior to breakdown (see Figure 4).

Junction Capacitance of Diode (Cj):

The space-charge region (or depletion region) of the diode is a region that contains very few holes or electrons and lies between the n-type semiconductor and the p-type semiconductor inside of the diode. The space-charge region of the diode approximates a parallel-plate capacitor, with the value of the capacitance determined by the applied voltage. Using this approximation, the capacitance of the space-charge region is approximately given by

nV

VC w eAC

bi

D jj

11 − 

  

 −== (5)

where e = permittivity of silicon (10 -12

F/cm),

A = cross-sectional area of the diode (cm 2

),

w = width of the depletion region (cm),

n = 2 for a step junction,

Vbi = built-in voltage, and

Cjo = the junction capacitance at VD = 0 V.

The junction capacitance is inversely proportional to w. As the reverse-bias voltage increases, the space-charge region widens, approximately as the square root of the applied voltage, and, thus, the capacitance decreases. This variation in w causes the diode to behave as a voltage-controlled capacitor with a capacitance that varies inversely with the square root of the applied voltage. If the diode had a very large cross-sectional area, the capacitance of the space-charge region as a function of the reverse voltage could be measured on an impedance bridge. Since the diodes in your lab are generally relatively small, it is very difficult to measure the voltage variation of the diode capacitance. Usually only a large area diode is large enough to be used to measure the diode capacitance using the lab equipment. Due to the large forward diode current, it is usually possible to measure the diode capacitance only for voltages less than Vγ.

EXPERIMENT:

PART I: MEASUREMENT OF DIODE CHARACTERISTICS

A. Forward I-V Characteristic

Procedure 1. Use the curve tracer to obtain the forward characteristics of the silicon 1N4004 diode.

• Connect diode cathode and anode terminals to terminals E and C, respectively, and set software switch to FET).

• Set the voltage axis to Vmax = 2 V.

• Begin your measurements with Imax = 2 mA.

• Use Pmax = 0.5 W.

• Press the start button to obtain the curve.

• Using the cursor key, take readings from the I-V characteristic for values of current close to those in the first column of Table 1, to enable you to plot accurately the I-V characteristic both on linear graph paper and on logarithmic graph paper. Increase the IMAX by a factor of 10 between measurements once you cannot read a higher value on the given curve. Tabulate your results below.

TABLE 1.1: Table of Current, voltage, forward resistance, dynamic resistance

ID (A) Your Value of ID (A) VD (volts) RF (Ω) = VD/ID rd (Ω) = nVT/ID 30µA

100µA 200 µA 400 µA

1mA 2mA 6mA

14mA 30mA 60mA 100mA 150mA

2. Compute RF and rd using the values you recorded and record in the table above. See Introduction for

the definitions of RF and rd.

B. Reverse I-V Characteristic

You should use the 1N4744 diode (Zener Diode) for this part of the experiment. If you use the 1N4004 diode, your breakdown voltage will be more negative than -100 V and diode breakdown cannot be seen on lab curve tracer. Also, the reverse leakage current will be very low for all of these silicon diodes, and such extremely low current cannot be measured with curve tracer.

Procedure

1) Turn off the power to the diode. Reverse the voltage polarity on the diode by turning the diode around in the socket and set Imax to 2 mA, Vmax to 40V, and Pmax to 0.5 W. Press the start button to obtain the reverse characteristics.

2) Sketch the reverse I-V characteristic as accurately as possible up to the breakdown voltage, noting the breakdown voltage on your plot.

PART 2: SIMPLE DIODE CIRCUITS

You should have simulated the diode-resistor circuit shown in Figure 5 with the values of R given below.

Figure 5: Simple Diode Circuit.

Procedure

1) Build the circuit shown in Figure 5 on the breadboard with R = 100 Ω. Use the 1N4001 or the 1N4004 diode.

2) Use the digital multimeter (DMM) DC Voltage [V═] function to measure the output voltage, Vo, using the V-Ω and COM banana jacks.

3) Using the variable power supply (VPS) and vary the voltage SUPPLY+ from 0 to 5V in increments of 0.5V and record the output voltage.

4) Repeat steps (1) to (3) for the other values of R given in Figure 5 and complete Table 2, below.

Table 2: Measured Vo for circuit in Figure 5

Vin (volts) Vo (volts)

R = 100Ω R = 1kΩ R = 10kΩ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

LAB REPORT:

PART I

1) Plot ID vs. VD on linear graph paper (or using software of your choice).

2) Determine Vγ directly from the plotted graph and record your result. Determine how Vγ depends on the diode current and voltage levels.

3) Determine the slope from the linear plot of the forward I-V characteristic as a function of the diode current, as shown in Figure 4, using the data previously taken in Table 1. Note that the inverse of the slope, or rd, you measure is a function of where you choose the diode current. Obtain at least eight (8) slope data points.

4) Plot RF and rd from Table 1 as a function of diode current. How do RF and rd compare?

5) Create a semi-log graph of ID (log scale) versus VD. Determine n from the slope. Remember that on a semi-log plot where I is plotted as a function of VD, an exponential function is a straight line. Use Equation (1) to determine n. Note that if n = 1, the current will increase by 1 decade for every 0.060V of VD, and if n = 2, the

current will increase by 1 decade for every 0.120V of VD. Extrapolate the current to VD = 0V and determine the value of IS.

PART II 1) What is the effect of the diode on Vo?

2) Derive an expression for Vo as a function of Vin using the piecewise-linear model of the diode comprised of the values of rd and Vγ you calculated from the linear I-V characteristic plot.

3) Compare the measured Vo with the simulated output voltage and the calculated output voltage from step II.2. Comment on any differences. Remember that the PSpice simulation is a simulation and is only as good as the parameters you use to describe the diode. Your experimental results are reality. You should be comparing the voltages you measured with the values you calculated using the measured diode characteristics.

EXPERIMENT CHECK LIST

1) Diode Characteristics

a) Forward Characteristics (VMAX = 2 V)

i) Obtain forward diode characteristics on curve tracer.

ii) Record linear and log current data points using cursor.

iii) Plot I-V characteristic (linear and semi-log).

iv) Determine rd as a function of diode current.

v) Determine RF as a function of diode current.

vi) Determine Vγ. How does Vγ change with diode current?

b) Reverse Characteristics

i) Attempt to obtain reverse diode characteristics. Set VMAX = 40 V.

ii) Is the breakdown voltage greater than 100 V?

2) Simple Diode Circuits

a) Build Circuit

b) Measure output (Vo) as a function of input voltage for R = 100 Ω, 1 kΩ, and 10 kΩ.

c) Derive an expression for Vo and Vin using piecewise model.

d) Compare measured results of Vo with simulated results and calculated output voltage.

PURPOSE:
PRE-LAB:
EQUIPMENT:
INTRODUCTION:
EXPERIMENT:
LAB REPORT:
EXPERIMENT CHECK LIST