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ELE230 Electronics I
http://www.ee.hacettepe.edu.tr/∼usezen/ele230/
Dr. Umut Sezen & Dr. Dinçer Gökcen
Department of Electrical and Electronic Engineering Hacettepe University
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 1 / 54
Course Contents
I (^) Semiconductor Diodes and Diode Applications I (^) DC and AC Analysis of Bipolar Junction Transistors (BJTs) I (^) DC and AC Analysis of Field Eect Transistors (FETs) I (^) Small-Signal Analysis of BJT and FET Ampli ers I (^) Frequency Response of BJT and FET Ampli ers I (^) Multistage Ampli ers
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 2 / 54
Textbook
Textbooks:
- Boylestad and Nashelsky, Electronic Devices and Circuit Theory , Prentice Hall, 8th ed.
- Sedra and Smith, Microelectronic Circuits, Oxford Press, 2009 (6th ed.)
Supplementary books:
- Millman and Halkias, Integrated Electronics, McGraw-Hill.
- Horowitz and Hill, The Art of Electronics, Cambridge, 3rd ed.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 3 / 54
Semiconductor Diodes Contents Semiconductor Diodes Semiconductor Diodes Ideal Diode Model p-n Junction Diodes No Bias Condition Reverse Bias Condition Forward Bias Condition Diode Characteristic Equation Zener Region (or Avalanche Breakdown Region) Peak Inverse Voltage (PIV) Rating Forward Bias Turn-On Voltage (VD(ON )) Temperature Eects Load Line and Operating Point (Q-point) DC Resistance (Static Resistance) AC Resistance (Dynamic Resistance) DC and AC Analysis Average AC Resistance Piecewise-Linear Equivalent Circuit Simpli ed Diode Model Diode Speci cation Sheets Semiconductor Notation Capacitance Other Types of Diodes Zener Diode Light Emitting Diode (LED) Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 4 / 54
Semiconductor Diodes Semiconductor Diodes
Semiconductor Diodes
Diode is a nonlinear two-terminal device whose circuit symbol is like an arrowhead shown below.
I (^) Voltage across the diode, VD , is normally de ned as the voltage dierence between back end of the arrowhead and front end of the arrowhead (voltage dierence between terminal A and terminal B), i.e., VD = VA − VB.
I (^) Current through the diode, ID , is de ned in the direction of the arrowhead ( owing from terminal A to terminal B), i.e., ID = IAB.
I (^) Diode is called forward biased (FB) when VA ≥ VB , i.e., VD ≥ 0 , and called reverse biased (RB) when VA < VB , i.e., VD < 0.
Semiconductor Diodes Ideal Diode Model
Ideal Diode Model
Ideally diode conducts current in only one direction and blocks current in the opposite direction. Thus,
I (^) Ideal diode is short circuit (i.e., ON) when it is forward biased.
and open circuit (i.e., OFF) when it is reverse biased.
Semiconductor Diodes Ideal Diode Model
Consequently, characteristics curve of the ideal diode is given by
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 7 / 54
Semiconductor Diodes Ideal Diode Model
Ideal Diode Summary
Diode state =
ON, if VD ≥ 0 OF F, if VD < 0
Ideal Diode Model State Circuit Behaviour Test Condition ON VD = 0 ID ≥ 0
OFF ID = 0 VD < 0
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 8 / 54
Semiconductor Diodes Ideal Diode Model
If you make a wrong assumption about the state of the diode, then you will nd that the test condition will fail (once you calculate the circuit voltage and currents). I (^) For example, if you have assumed the diode to be ON while it should be OFF, then you will nd ID < 0 , failing the test condition. I (^) Similarly, if you have assumed the diode to be OFF while it should be ON, then you will nd VD ≥ 0 , failing the test condition.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 9 / 54
Semiconductor Diodes Ideal Diode Model
Example 1: Consider the circuit below and nd ID and VD. Assume the diode is ideal.
Solution: First we need to determine the state of the ideal diode (i.e., ON or OFF). So, let us write down the KVL equation and obtain VD
VD = 5 − 5 ID
As it is seen from the equation above, VD ≥ 0. So, the diode is ON. Thus,
VD = 0 V... from circuit behaviour
ID = 5 − VD 5 = 5 − 0 5 = 1 A.
We see that test condition ID ≥ 0 is satis ed, so our solution is correct.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 10 / 54
Semiconductor Diodes Ideal Diode Model
Assume we made a mistake and assumed the diode is OFF. Then, we would nd that
ID = 0 A... from circuit behaviour VD = 5 − 5 ID = 5 − (5)(0) = 5 V.
We see that the test condition VD < 0 fails. That means our assumption is wrong, i.e., diode is not OFF, it is ON.
Then, we go back and correct our assumption and take the diode is ON and perform the appropriate steps (as we did in the correct solution) and nd the correct result as VD = 0 V and ID = 5 A.
Semiconductor Diodes p-n Junction Diodes
p-n Junction
In an n-type semiconductor, majority carriers are electrons and minority carriers are holes.
Similarly, in a p-type semiconductor, majority carriers are holes and minority carriers are electrons. When we join n-type and p-type semiconductors (Silicon or Germanium) together, we obtain a p-n junction as shown below.
Current formed due to the movement of majority carriers across the junction is called the majority carrier current, Imajority. Similarly, current formed due to the movement of minority carriers across the junction is called the minority carrier current, Is. Note that, minority carrier and majority carrier currents ow in opposite directions.
Semiconductor Diodes p-n Junction Diodes
I (^) Forward bias circuit behaviour is also shown below
I (^) Thus, diode current ID under forward bias is given by
ID = Imajority − Is.
I (^) Normally Imajority Is, so diode current ID under forward bias is approximately equal to the majority carrier current, i.e.,
ID ≈ Imajority.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 19 / 54
Semiconductor Diodes p-n Junction Diodes
Diode Characteristic Equation
Empirically obtained diode characteristics curve covering all three operating conditions is shown below
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 20 / 54
Semiconductor Diodes p-n Junction Diodes
I (^) Diode characteristic equation (also known as the Shockley diode equation) describing the diode characteristics curve is given below
ID = Is
eVD^ /γ^ − 1
where γ, sometimes expressed as VT , is the thermal voltage given by
γ = kT q
with k, q and T being the Boltzman constant, the charge of an electron and temperature in Kelvins, respectively. Note that, kq is constant given by
k q
= η 8. 6173 × 10 −^5 V/K
where η = 1 for Ge and η = 2 for Si for relatively low levels of diode current (at or below the knee of the curve) and η = 1 for Ge and Si for higher levels of diode current (in the rapidly increasing section of the curve). We can safely assume η = 1 for most cases.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 21 / 54
Semiconductor Diodes p-n Junction Diodes
I (^) Under forward bias, diode characteristic equation simpli es (as eVD /γ^ 1 ) to the simpli ed forward bias diode equation below
ID ≈ IseVD^ /γ I (^) Under reverse bias, diode characteristic equation simpli es (as eVD^ /γ^ 1 ) to the following ID ≈ −Is I (^) Note that, γ only depends on the temperature (expressed in Kelvin units).
So, thermal voltage γ at room temperature T = 300 K (i.e., T = 27 ◦C) is given by
γ = γ |T =300 K = 26 mV.
If we take the room temperature as T = 25 ◦C, then thermal voltage becomes
γ |T =298 K = 25 mV.
NOTE: Temperature in Kelvin (T ) is obtained from the temperature in Celsius (TC ) as follows T = TC + 273
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 22 / 54
Semiconductor Diodes p-n Junction Diodes
Zener Region (or Avalanche Breakdown Region)
As the voltage across the diode increases in the reverse-bias region, the velocity of the minority carriers responsible for the reverse saturation current Is will also increase. Eventually, their velocity and associated kinetic energy will be su cient to release additional carriers (i.e., avalanche eect) through collisions with otherwise stable atomic structures. That is, an ionization process will result whereby valence electrons absorb su cient energy to leave the parent atom. These additional carriers can then aid the ionization process to the point where a high avalanche current is established and the avalanche breakdown region determined.
Semiconductor Diodes p-n Junction Diodes
The avalanche region (VZ ) can be brought closer to the vertical axis by increasing the doping levels in the p- and n-type materials. However, as VZ decreases to very low levels, such as 5 V, another mechanism, called Zener breakdown, will contribute to the sharp change in the characteristic. It occurs because there is a strong electric eld in the region of the junction that can disrupt the bonding forces within the atom and generate carriers generally via tunnelling (sometimes called as tunnelling breakdown) of the majority carriers under reverse-bias electric eld when the valence band of the highly doped p-region is aligned with the conduction band of the highly doped n-region. Although the Zener breakdown mechanism is a signi cant contributor only at lower levels of VZ , this sharp change in the characteristic at any level is called the Zener region and diodes employing this unique portion of the characteristic of a p-n junction are called Zener diodes.
Semiconductor Diodes p-n Junction Diodes
Peak Inverse Voltage (PIV) Rating
Avalanche breakdown region of the semiconductor diode must be avoided if the diode is supposed to work as an ON and OFF device. The maximum reverse-bias potential that can be applied before entering the avalanche breakdown region is called the peak inverse voltage (referred to simply as the PIV rating ) or the peak reverse voltage (denoted by PRV rating).
If an application requires a PIV rating greater than that of a single unit, a number of diodes of the same characteristics can be connected in series. Similarly, diodes can be also connected in parallel to increase the current-carrying capacity.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 25 / 54
Semiconductor Diodes p-n Junction Diodes
Forward Bias Turn-On Voltage (VD(ON ))
The point at which the diode changes from No Bias condition to Forward Bias condition happens when the electron and holes are given su cient energy to cross the p-n junction. This energy comes from the external voltage applied across the diode.
This voltage (can be deduced from the diode characteristics curve) is called the turn-on voltage or the threshold voltage, and denoted by VD(ON ) (VT or V 0 notations are also used).
The forward bias voltage required to turn on the diode for a
Silicon diode: VD(ON ) = 0. 7 V
Germanium diode: VD(ON ) = 0. 3 V
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 26 / 54
Semiconductor Diodes p-n Junction Diodes
Temperature Eects
I (^) As temperature increases it adds energy to the diode. From the gure above, as temperature increases
It reduces the required turn-on voltage (VD(ON )) in forward bias condition, It increases the amount of reverse saturation current (Is) in reverse bias condition, (^) It increases the avalanche breakdown voltage in reverse bias condition.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.)^ I^ Germanium diodes are more sensitive to temperature variations than Silicon diodes. ELE230 Electronics I 15-Feb-2017 27 / 54
Semiconductor Diodes p-n Junction Diodes
Load Line and Operating Point (Q-point)
From the gure on the left above, we obtain
VD = E − ID R I We can rearrange the circuit equation above to get ID on the left-hand side of the equation, i.e.,
ID =
R
VD +
E
R
I (^) This equation obtained from the diode circuit is called the load line equation.
The load line equation gives us all the possible current (ID ) values for all the possible voltage (VD ) values obtained across the diode in a given circuit.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 28 / 54
Semiconductor Diodes p-n Junction Diodes
I (^) Once we draw the load line over the diode characteristics curve given in the gure on the right in the previous slide, and the intersection point will give us the solution (IDQ, VDQ) of the diode current and diode voltages ID and VD for the given circuit, respectively. The result is shown below.
I (^) This plot is called the load line plot. Also, the intersection point of the load line and the diode characteristics curve is called the operating point or the Q-point speci ed by the (IDQ, VDQ) pair. Note that Q stands for quiescent (i.e., still). I (^) For some examples, see Examples 2.1, 2.2 and 2.3 in the Boylestad and Nashelsky textbook (8th ed.).
Semiconductor Diodes p-n Junction Diodes
A load line plot like the gure in the previous slide is actually the graphical way of solving the diode characteristics equation
ID = IS
e VD /γ − 1
and the electrical circuit equation, i.e., load line equation
ID = −
VD
R
E
R
simultaneously. Load line plots are very practical and more e cient than solving these two equations analytically.
Semiconductor Diodes p-n Junction Diodes
I We obtain small signal AC analysis circuit by killing the DC sources as shown below
I (^) In AC analysis, diode is replaced by its dynamic resistance rd and we can nd id(t) and vd(t) as follows
id(t) = vac(t) R + rd vd(t) = rd R + rd vac(t).
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 37 / 54
Semiconductor Diodes p-n Junction Diodes
Average AC Resistance
I (^) Average AC resistance can be determined by picking two points on the characteristic curve developed for a particular circuit where the voltage and current variations (i.e., ∆Vd and ∆Id) are large. It is used to develop the piecewise-linear equivalent circuit of the diode. I (^) Thus, the average AC resistance rav is calculated as
rav = ∆VD ∆ID (point-to-point)
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 38 / 54
Semiconductor Diodes Piecewise-Linear Equivalent Circuit
Piecewise-Linear Equivalent Circuit
I (^) Piecewise-linear approximation of the diode characteristics curve is obtained and depicted as the blue lines on the left of the gure above.
I (^) Similarly, obtained piecewise-linear equivalent circuit is shown on the right of the gure above.
I (^) Here, rav is the forward bias average AC resistance (i.e., internal resistance) of the diode.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 39 / 54
Semiconductor Diodes Simpli ed Diode Model
Simpli ed Diode Model
I (^) Simpli ed diode characteristics curve is obtained and shown on the left of the gure above.
I (^) Similarly, obtained simpli ed equivalent circuit is shown on the right of the gure above.
Diode state =
{ ON, if VD ≥ VD(ON ) OF F, if VD < VD(ON )
Simpli ed Diode Model State Circuit Behaviour Test Condition ON VD = VD(ON ) ID ≥ 0 OFF ID = 0 VD < VD(ON )
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 40 / 54
Semiconductor Diodes Simpli ed Diode Model
I (^) For the ideal diode model, the turn-on voltage is zero, i.e., VD(ON ) = 0 V.
In this course, we will mostly use the simpli ed diode model unless otherwise stated.
Semiconductor Diodes Simpli ed Diode Model
Example 2: Consider the circuit below and nd ID and VD with VD(ON ) = 0. 7 V and E > 0. 7 V.
Solution: First we need to determine the state of the diode (i.e., ON or OFF). So, let us write down the KVL equation and obtain VD
VD = E − ID R
As it is seen from the equation above, VD ≥ VD(ON ). So, the diode is ON. Thus,
VD = VD(ON ) = 0. 7 V... from circuit behaviour
ID = E − VD R = E − 0. 7 R VR = E − VD = E − 0. 7
Semiconductor Diodes Simpli ed Diode Model
As E > 0. 7 V is given, we see that test condition ID ≥ 0 is satis ed. So, our solution is correct.
Thus, our diode circuit is simpli ed to the circuit shown below
Note that IR = ID.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 43 / 54
Semiconductor Diodes Simpli ed Diode Model
Example 3: Consider the circuit below and nd ID and VD with VD(ON ) = 0. 7 V and E > 0. 7 V.
Solution: First we need to determine the state of the diode (i.e., ON or OFF). So, let us write down the KVL equation and obtain VD
VD = −E − ID R
As it is seen from the equation above, VD < VD(ON ). So, the diode is OFF. Thus,
ID = 0 A... from circuit behaviour VD = −E − ID R = −E VR = −ID R = 0 V
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 44 / 54
Semiconductor Diodes Simpli ed Diode Model
As E > 0. 7 V is given, we see that test condition VD < 0 is satis ed. So, our solution is correct.
Thus, our diode circuit is simpli ed to the circuit shown below
Note that IR = −ID = 0 A.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 45 / 54
Semiconductor Diodes Simpli ed Diode Model
Example 4: Consider the circuit below and nd I 1 , Vo, ID 1 and ID 2 with VD(ON ) = 0. 7 V and D 1 ≡ D 2.
Solution: First we need to determine the state of the diodes (i.e., ON or OFF). As the diodes are parallel, we let us make the following de nitions
VD = VD 1 = VD 2 ID = ID 1 + ID 2 = I 1 So, let us write down the KVL equation and obtain VD
VD = E − ID R = 10 − 0. 33 k ID
As it is seen from the equation above, VD ≥ VD(ON ). So, both diodes are ON.
Dr. U. Sezen & Dr. D. Gökçen (Hacettepe Uni.) ELE230 Electronics I 15-Feb-2017 46 / 54
Semiconductor Diodes Simpli ed Diode Model
Thus,
VD 1 = VD(ON ) = 0. 7 V... from circuit behaviour VD 2 = VD(ON ) = 0. 7 V... from circuit behaviour Vo = VD = 0. 7 V
I 1 = E − VD R
= 10 − 0. 7
- 33 k
= 28. 18 mA
ID 1 = ID 2 = I 1 2 = 14. 09 mA... as D 1 ≡ D 2
Exercise: What will happen if D 2 is replaced by a Germanium diode?
Semiconductor Diodes Diode Speci cation Sheets
Diode Speci cation Sheets
Data about a diode is presented uniformly for many dierent diodes. This makes cross-matching of diodes for replacement or design easier.
Some of the key elements is listed below:
- VF : forward voltage at a speci c current and temperature
- IF : maximum forward current at a speci c temperature
- IR: maximum reverse current at a speci c temperature
- PIV or PRV or VBR: maximum reverse voltage at a speci c temperature
- Power Dissipation: maximum power dissipated at a speci c temperature
- C: Capacitance levels in reverse bias
- trr : reverse recovery time
- Temperatures: operating and storage temperature ranges
