University of Pittsburgh

Experiment #4 Lab Report

Diode Characteristics and Circuit Models

Submission Date:

10/2/2017

Instructors:

Dr. Minhee Yun

John Erickson

Yanhao Du

Submitted By:

Nick Haver & Alex Williams

Station #16

ECE 1201: Electronic Measurements and Circuits Laboratory

Introduction

In this experiment we measured voltage and current characteristics of standard silicon diodes, light-emitting diodes (LEDs),

and Zener diodes. Diodes were placed in circuits along with resistors in several different topologies. Due to the fact that

diodes have generally low resistances compared to the 100Ω and 1000Ω resistors used in this lab, the multimeter was used

to measure voltage across resistors, rather than the diode itself as to not interfere with the actual resistance of the diode.

Kirchoff’s voltage law and Ohm’s law could then be applied to determine diode voltages and currents.

Procedure A

I. For the circuit shown in Figure 1, diode voltage (VD) was calculated for a series of source voltages (Vi) from -

10 V to +10V. First, the voltage across the 100Ω resistor (VAB) was measured with the digital multimeter. Then

using Kirchoff’s voltage law, VD was calculated as follows:

𝑉𝐷 = 𝑉𝑖 − 𝑉𝐴𝐵 (1)

Table 1 shows the VAB measured for each Vi, VD calculated using Equation 1, and diode current ID calculated

as follows:

𝐼𝐷 =𝑉𝐴𝐵

100 𝛺 (2)

Figure 1: Circuit Constructed and Measured for Procedure A

Table 1: Measured VAB and Calculated VD and ID for Each Vi for Si Diode

Vi (V) VAB (mV) VD (mV) ID (mA)

-10.0 -0.0250 -9999.9750 -0.0003

-5.0 -0.0250 -4999.9750 -0.0003

0.1 0.0000 100.0000 0.0000

0.2 0.0150 199.9850 0.0002

0.3 0.1750 299.8250 0.0018

0.4 1.4750 398.5250 0.0148

0.5 10.5500 489.4500 0.1055

0.6 42.6900 557.3100 0.4269

0.7 99.1200 600.8800 0.9912

0.8 168.4550 631.5450 1.6846

0.9 247.4000 652.6000 2.4740

1.0 328.0000 672.0000 3.2800

3.0 2192.0000 808.0000 21.9200

5.0 4132.0000 868.0000 41.3200

8.0 7076.0000 924.0000 70.7600

10.0 9048.0000 952.0000 90.4800

II. Diodes are commonly modeled by Equation 3 shown below. Using the data gathered in Part I, IS and nVT were

calculated to develop and I-V characteristic equation for the specific diode used. To do this, ID and VD were

plotted and fit with an exponential trendline (Equation 4), as shown in Figure 2.

𝐼𝐷 = 𝐼𝑆(𝑒𝑉𝐷

𝑛𝑉𝑇 − 1) (3)

𝑦 = (1.4349 × 10−5)𝑒(1.7467×10−2) 𝑥 (4)

Equation 3 was then fit with the constants from the plot’s exponential trendline to determine the following I-V

characteristics for the diode:

𝐼𝑆 = (1.4349 × 10−5)𝐴 = 0.014349 𝑚𝐴 (5)

𝑛𝑉𝑇 =1

(1.7467 × 10−2) 𝑉 = 57.2508 𝑉 (6)

𝐼𝐷 = (1.4349 × 10−5) (𝑒𝑉𝐷

57.2508 𝑉 − 1) 𝐴 (7)

III. Diodes operating in the forward region are commonly modeled with the I-V characteristic shown in Figure 3:

Figure 3: Forward Region Linear Diode Model Circuit and I-V Curve

0

50

100

150

200

250

300

0 200 400 600 800 1000

I D(m

A)

VD (mV)

ID vs VD

To calculate VDO and RD for the I-V curve shown in Figure 3, the last 4 data plots were plotted as shown I

Figure 4:

Figure 4: I-V Curve with Linear Trendline to Calculate VDO and RD

Using the trendline of the plot shown in Figure 4, RD and VDO were calculated:

𝑦 = 0.4723𝑥 − 363.27

(8)

𝑅𝐷 =1

0.4723= 2.1173 𝛺 (9)

𝑉𝐷𝑂 = 769.151 𝑚𝑉 (10)

Conclusion

The results from parts one through three were as expected. When the diode was reverse biased it did not allow current

through and so had the same voltage across it as the source voltage. This can be discerned by the measurements across the

resistor, as the two are in series, so the voltage across the resistor and the voltage across the diode add up to the source

voltage. Once in the forward biased region, the diode began two follow the exponential equation at about 700 mV. This is

to be expected, as the diode is non-ideal so there is about a 700 mV activation voltage. Examining the curve tracker

measurements, the diode follows the same curve that was experimentally determined by taking a series of measurements

with the ohmmeter.

0

10

20

30

40

50

60

70

80

90

100

800 850 900 950 1000

I D(m

A)

VD (mV)

ID VS VD

Procedure B

IV. The two circuits shown in Figure 5 were constructed on the breadboard. The current through each of diodes

was measured using the ammeter feature of the digital multimeter. To do this, the multimeter was placed in

series with the diode to be measured.

Figure 5: The Diode Circuits Evaluated in Procedure B

Diode currents for each of the didoes in circuits A and B were measured as follows:

Table 2: Measured Current for the Diodes in Circuit A and Circuit B

Circuit A Circuit B

Diode Current Diode Current

Diode 1 0.007 µA Diode 1 4.358 mA

Diode 2 2.203 mA Diode 2 4.573 µA

Diode 3 4.573 µA

Using the RD and VDO parameters found in Procedure A, the linear model was applied to Circuit A and Circuit

B and diode currents were calculated using this model. For Circuit A, diode currents were calculated to be:

𝐼𝐷1 = 0 𝐴 𝐼𝐷2 = 2.1154 𝑚𝐴 (11)

These calculated values were consistent with our measured values of 0.007 µA and 2.203 mA. For Circuit B,

diode current 1 was calculated to be:

𝐼𝐷1 = 4.2308 𝑚𝐴 (12)

This calculated value is consistent with our measured value of 4.358 mA. For diodes 2 and 3, however, applying

the linear model results in a current divider between the two parallel branches in Circuit B. Calculating ID2 and

ID3 using this model will give a value of approximately 2 mA, not the 4.573 µA that was measured. This is

because, in Circuit B, diodes 2 and 3 are not operating, but are turned off.

The linear model most accurately represents diodes in the operating forward-bias region. As a result, applying

the linear model to a “turned off” diode yields a result inconsistent with observed current measurements.

V. For Part 5, the I-V characteristic of a light-emitting diode (LED) was measured and plotted using the same

procedure as used in Part 1, as shown in Table 3 and Figure 6.

Figure 6: Circuit Constructed and Measured for Part 5

Table 3 shows VD and ID, which were calculated as follows:

𝑉𝐷 = 𝑉𝑖 − 𝑉𝐴𝐵 (13)

𝐼𝐷 =𝑉𝐴𝐵

𝑅=

𝑉𝐴𝐵

100 𝛺 (14)

Table 3: Measured VAB and Calculated VD and ID for Each Vi for LED

Vi (V) VAB (mV) VD (mV) ID (mA)

-10.0 -0.0090 -9999.9910 -0.0001

-5.0 -0.0090 -4999.9910 -0.0001

1.0 -0.0090 1000.0090 -0.0001

1.5 16.8000 1483.2000 0.1680

1.7 127.8000 1572.2000 1.2780

1.8 205.3000 1594.7000 2.0530

2.0 376.0000 1624.0000 3.7600

4.0 2284.0000 1716.0000 22.8400

6.0 4248.0000 1752.0000 42.4800

8.0 6217.0000 1783.0000 62.1700

10.0 8191.0000 1809.0000 81.9100

Figure 7: I-V Curve for VD > 0 with Linear Trendline to Calculate VDO and RD

Figure 7 shows a plot of ID vs VD for VD > 0. Fitting a linear trendline to this data gives the equation:

𝑦 = 0.0803𝑥 − 103.84 (15)

Setting the trendline equal to zero gives VDO and RD can be calculated as the inverse of the slope as follows:

0.0803𝑥 − 103.84 = 0

𝑥 = 𝑉𝐷𝑂 = 1293.15 𝑚𝑉 = 1.293 𝑉

(16)

𝑅 =1

0.0803= 12.45 𝛺 (17)

Compared to the silicon diode, both VDO and RD are greater for the light-emitting diode. As forward diode

current is increased, power dissipated is increased, and therefore, light output is increased.

Conclusion

The LED functioned the same as the diode when reverse biased, letting effectively no current through. When forward biased

however, the LED had approximately double the required voltage to begin operating effectively. The exponential curve

began to rise after 1.5 V. However, once in the operating region, the curve functioned the same as the original diode. As

expected, when the source voltage was increased and more current flowed through the LED it glowed brighter. To get a

specific current, one should use a 1000 Ω resistor in series with the LED and use the following equation to determine the

source voltage for whatever is the goal current ID = 1E-13e0.0191Vd – 1.5 Vd.

-40

-20

0

20

40

60

80

100

0 500 1000 1500 2000

I D(m

A)

VD (mV)

ID VS VD

Procedure C

VI. For Part 6, the Zener diode circuit shown in Figure 8 was constructed with R=150Ω.

Figure 8: Circuit Constructed and Measured for Part 6

Table 4 shows the measured Vps and VAB, as well as VD and ID, which were calculated using the following

equations:

𝑉𝐷 = 𝑉𝑝𝑠 − 𝑉𝐴𝐵 (18)

𝐼𝐷 =𝑉𝐴𝐵

𝑅=

𝑉𝐴𝐵

150𝛺 (19)

Table 3: Measured VAB and Calculated VD and ID for Each Vps for Zener Diode

Vps (V) VAB (mV) VD (mV) ID (mA)

-10.0 -9153.00 -847.00 -61.02

-8.0 -7163.00 -837.00 -47.75

-6.0 -5177.00 -823.00 -34.51

-4.0 -3190.00 -810.00 -21.27

-2.0 -1222.00 -778.00 -8.15

-1.5 -736.00 -764.00 -4.91

-1.0 -264.00 -736.00 -1.76

-0.8 -94.68 -705.32 -0.63

-0.7 -30.43 -669.57 -0.20

-0.6 -3.65 -596.35 -0.02

-0.5 -0.28 -499.71 -0.01

1.0 0.60 999.40 0.01

1.5 10.10 1489.90 0.07

1.7 23.90 1676.10 0.16

1.9 49.30 1850.70 0.33

2.1 90.20 2009.80 0.60

2.3 148.70 2151.30 0.99

2.5 224.80 2275.20 1.50

3.0 478.90 2521.10 3.19

3.5 800.70 2699.30 5.34

4.0 1160.00 2840.00 7.73

4.5 1547.00 2953.00 10.31

5.0 1956.00 3044.00 13.04

6.0 2813.00 3187.00 18.75

7.0 3700.00 3300.00 24.67

8.0 4609.00 3391.00 30.73

9.0 5536.00 3464.00 36.91

10.0 6478.00 3522.00 43.19

Plotting VD = Vz and ID = Iz from Table 3 (as shown in Figure 9) and fitting with a fifth-order polynomial gives

the equation:

𝑦 = (2.79 × 10−15)𝑥5 + (2.18 × 10−11)𝑥4 + (5.71 × 10−8)𝑥3 + (4.61 × 10−5)𝑥2

− (1.92 × 10−2)𝑥 − 26.45 (20)

Solving for the roots of this equation gives VZO = 1834.82 mV for -VZO where IZ < 0.

Figure 9: IZ vs VZ Plot for Zener Diode with Fifth-Degree Polynomial Trendline

Considering only the points for which VZ is less than zero, a linear equation can be fit to the IZ-VZ data (shown in

Figure 10) with the equation:

𝑦 = 0.0231𝑥 + 50.538 (21)

Given that RZ is the inverse of the slope of this equation:

𝑅𝑍 =1

0.0231= 43.290𝛺 (22)

-60

-40

-20

0

20

40

60

80

-4000 -3000 -2000 -1000 0 1000 2000

IZ VS VZ

Figure 10: IZ vs VZ Plot for Zener Diode for VZ > 0 with Linear Trendline

Zener diodes may be particularly useful in voltage clamping circuits. This is because the diode can function when

the voltage is both greater than or less than zero. For a particular diode or series of diodes, certain voltage limits

can be defined for which the diode will conduct.

VII. Figure 11 shows two lines, both of which are for a defined Vps = 3.0V and R=150Ω. The orange line is the load

line, defined as:

𝐼𝐷 =𝑉𝑝𝑠

𝑅−

𝑉𝐷

𝑅= −0.0067𝑥 + 20 𝛺−1 (23)

Figure 11: I-V Curve and Load Line for Vps = 3.0 V

The blue line is an exponential fit of the Zener diode IZ-VZ data for VZ > 0. This line can be defined using the

equation:

𝑦 = 0.0005𝑒0.0034𝑥 (24)

-50

-40

-30

-20

-10

0

10

20

-4000 -3000 -2000 -1000 0

IZ VS VZ

-20

-10

0

10

20

30

40

50

60

70

0 1000 2000 3000 4000 5000

I D(m

A)

VD (mV)

ID vs VD for Vps=3.0V

Setting Equation 23 and Equation 24 equal gives the operating point of the Zener diode at Vps = 3.0 V and

R=150Ω. The operating point in this case was calculated to be:

−0.0067𝑥 + 20 = 0.0005𝑒0.0034𝑥

𝑥 = 2550.14 𝑚𝑉 (25)

Conclusion

The Zener diode is the only diode that showed noticeable current running through it when reverse biased, which is the

expected result. When reverse biased, it followed a slower exponential trend line than when in the forward biased region

which is standard for a Zener diode. For use in clamping circuits, Zener diodes can be put in parallel with a whatever load

circuit is being used, so that when a source voltage is applied the Zener diode is reverse biased. This way, the diode will act

as on open circuit with no current passing through it for lower voltages, however if the voltage increases, the Zener diode

will begin to siphon off excess current from the main circuit. For circuits that operate at higher voltages, Zener diodes can

be put in series to increase the required activation voltage, in the case of the Zener diode we used, it would be about 1.5

volts for every Zener diode in series.

Procedure D

VIII. The semiconductor curve tracer was used to measure the I-V characteristics of each of the three diodes used

in Lab 4. Figure 12 shows the I-V curve for the standard silicon diode. Figure 13 shows the I-V curve for the

light-emitting diode (LED). Figures 14 and 15 shows the I-V curves for the Zener diode operating in forward

and reverse bias, respectively. Figure 15 shows the diode voltage as positive, as the curve tracer only applies a

positive voltage. In practice however, the diode is operated in reverse bias when the diode voltage is less than

zero.

Figure 12: Silicon Diode I-V Curve

Figure 13: Light-Emitting Diode (LED) I-V Curve

Figure 14: Zener Diode Forward Bias I-V Curve

Figure 15: Zener Diode Reverse Bias I-V Curve

Table 4 compares the observed values of VDO from the curve tracer with those measured in the lab for each

diode type.

Table 4: Observed and Measured VDO for Each Diode Used in Lab 4

Diode Type Observed VDO (mV) Measured VDO (mV)

Standard Silicon 700 769

Light-Emitting (LED) 1600 1293

Zener (Reverse Bias) 1500 1835

Experiment Conclusion

The purpose of Experiment #4 was to measure voltage and current characteristics of standard silicon diodes, light-emitting

diodes, and Zener diodes. All three types were observed on the semiconductor curve tracer, and then through plotting and

analyzing measured data points. All three types of diodes chare similar characteristics during forward-biased operation. In

reverse-biased operation, only the Zener diode can operate over a range of voltage before reaching its breakdown voltage.

References

ECE 1201 Website: http://engrclasses.pitt.edu/electrical/faculty-staff/gli/1201/