Term Roadmap : Introduction to Signal Processing Differentiating and Integrating Circuits (OpAmps) Clipping and Clamping Circuits(Diodes) Design of analog filters Sinusoidal Oscillators Multivibrators Sampling and Quantization techniques of analog signals DACs and ADCs Data Acquisition Systems Introduction to discrete time transform and DSP The Z transform Design of Digital Filters 1. INSULATORS Materials Types An INSULATOR is any material that inhibits (stops) the flow of electrons (electricity). An insulator is any material with 5 to 8 free electrons in the outer ring. Because, atoms with 5 to 8 electrons in the outer ring are held (bound) tightly to the atom, they CANNOT be easily moved to another atom nor make room for more electrons. Insulator material includes glass, rubber, and plastic
2. CONDUCTORS Materials Types A CONDUCTOR is any material that easily allows electrons (electricity) to flow. A CONDUCTOR has 1 to 3 free electrons in the outer ring. Because atoms with 1 to 3 electrons in the outer ring are held (bound) loosely to the atom, they can easily move to another atom or make room for more electrons. Conductor material includes copper and gold 3. SEMICONDUCTORS Materials Types Any material with exactly 4 free electrons in the outer orbit are called SEMICONDUCTORS. A semiconductor is neither a conductor or insulator. Semiconductor material includes carbon, silicon, and germanium. These materials are be used in the manufacturer of diodes, transistors, and integrated circuit chips.
Semiconductor Diode Diode is formed by bringing these two material together p- and n-type. Holes diffuse from the p side to the n side, leaving behind negatively charged immobile negative ions. Electrons diffuse from the n side to the p side, leaving behind positively charged immobile positive ions. Electrons and holes at joined region will combine, resulting in a lack of carriers in the region near the junction (depletion region) Reverse-Bias Condition (VD < 0V) Reverse-biased p-n junction
Reverse-Bias Condition (VD < 0V) The number of positive ions in the depletion region of n-type will increase due to large number of free electrons drawn to the positive potential. The number of negative ions will increase in p-type resulting widening of depletion region. This region established great barrier for the majority carriers to overcome, resulting I majority =0 A very small amount of reverse current does flow, due to minority carriers diffusing from the (p/n) regions into the depletion region and drifting across the junction. Forward-Bias Condition (VD > 0V) Forward-biased p-n junction
Forward-Bias Condition (VD = 0V) A semiconductor diode is forward-biased when the association p-type and positive voltage and n-type and negative voltage has been established. The application of forward-bias potential will pressure the electrons in n-type and hole in p-type to recombine with ions near the boundary and reduce the width of depletion region The reduction in width of depletion region has resulted in a heavy majority flow across the junction Semiconductor Diodes Figure 3.39 Simplified physical structure of the junction diode. (Actual geometries are given in Appendix A.) Circuit symbol
Diodes Several types of diodes. The scale is centimeters The i v characteristic of a silicon diode. Figure 3.7 The i characteristic of a silicon junction diode. Figure 3.8 The diode i relationship with some scales expanded and others compressed in order to reveal details.
The i v characteristic of a silicon diode. The Forward-Bias region:- In the forward region the i- v relationship is closely approximated by.. kv T k i I s ( e 1) I s.the reverse saturation current ( scale current) K = Boltzmann`s constant = 1.38*10-23 joules / kelvin T k = the absolute temperature in kelvins = 273 + temperature in C The i v characteristic of a silicon diode. The Reverse-Bias region:- The exponential term becomes negligibly small compared to unity, and the diode current becomes.. i I s That is, the current in the reverse direction is constant and equal to Is which tends to zero. The Breakdown Region:- The breakdown region is entered when the magnitude of the reverse voltage exceeds a threshold value that is specific to the particular diode, called the breakdown voltage.
Ideal Diode Figure 3.1 The ideal diode: (a) diode circuit symbol; (b) i characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction. Figure 3.2 The two modes of operation of ideal diodes and the use of an external circuit to limit the forward current (a) and the reverse voltage (b). Modeling the diode forward characteristic The Piecewise-linear Model Figure 3.13 Piecewise-linear model of the diode forward characteristic and its equivalent circuit representation. Figure 3.12 Approximating the diode forward characteristic with two straight lines: the piecewiselinear model. Figure 3.14 The circuit of Fig. 3.10 with the diode replaced with its piecewiselinear model of Fig. 3.13.
Modeling the diode forward characteristic The Piecewise-linear Model Example: Given: V DD = 5V, V DO = 0.65, r D = 20,R= 1K Thus 5 0.65 I D 4. 26mA 1 0.02 V D = V DO +I D r D = 0.65+4.26x0.02=0.735V Modeling the diode forward characteristic The Constant-voltage-drop Model Figure 3.15 Development of the constantvoltage-drop model of the diode forward characteristics. A vertical straight line (B) is used to approximate the fast-rising exponential. Observe that this simple model predicts V D to within 0.1 V over the current range of 0.1 ma to 10 ma. Figure 3.16 The constant-voltage-drop model of the diode forward characteristics and its equivalent-circuit representation.
Modeling the diode forward characteristic The Ideal Diode Model Figure 3.1 The ideal diode: (a) diode circuit symbol; (b) i characteristic; (c) equivalent circuit in the reverse direction; (d) equivalent circuit in the forward direction. Operation in The reverse Breakdown Region- Zener Diodes Figure 3.20 Circuit symbol for a zener diode. Figure 3.22 Model for the zener diode. Figure 3.21 The diode i characteristic with the breakdown region shown in some detail.
Operation in The reverse Breakdown Region- Zener Diodes Example: Find I? Figure 3.23 (a) Circuit for Example 3.8. (b) The circuit with the zener diode replaced with its equivalent circuit model. Diode Applications
AND/OR Gates AND and OR gates represent basic components of computers that are used to implement Boolean algebra. OR-Gate 1 2 3 0 0 0 0 1 1 1 0 1 1 1 1 AND-Gate 1 2 3 0 0 0 0 1 0 1 0 0 1 1 1 If logic 1 is represented by +10 (+5) V and logic 0 is represented by 0 V, the OR and the AND gates can be represented by the following diode combinations; AND/OR Gates For the OR gate; D1 ON D2 OFF V 0 =10V ( logic 1) For the AND gate; D1 OFF D2 ON V 0 =0V ( logic 0)
Diodes Applications: Rectifier Circuits Figure 3.24 Block diagram of a dc power supply. Sinusoidal Inputs; Half-wave Rectification (Ideal diode Model) So far, we have considered time invariant signals only (DC). Now, diode circuit analysis will be extended to include circuits containing time varying signals (AC). The simplest diode application that uses AC signals is the HWR signal shown. To simplify the analysis, we ll assume that the diodes used are ideal. Note that, the DC content of the input waveform is zero, Why? During time interval t=0 T/2, diode is ON. Since we are using an ideal diode model, v 0 =v i. During the time interval t=t/2 T, diode is OFF; v 0 =0. Now, what is the value of the DC level in the output waveform? (V dc =0.318V m ) 5.0V 0V -5.0V 0s 1.0s 2.0s V(R5:2) V(V5:+) Time
HWR with Const Voltage Drop Diode Model In case of using the constant voltage drop diode model, during the conduction period diode will be replaced with a constant voltage source V D0. Thus, the peak of the output waveform will decrease from V s by V D0. In addition, the conduction period of the diode will be slightly less than T/2. In this case, the DC content of the output waveform becomes; V dc 0.318(V s -V D0 ) (Note:0.318V s =V s / ) (Vs i.e Vm, VD0 i.e VT) Peak Inverse Voltage (PIV) Definition: PIV is the value of the maximum reverse voltage that is expected to apply to the diode in during its operation. PIV: Peak Inverse Voltage in this case = V s, Thus, PIV rating >V s The rectifier with a filter capacitor
The rectifier with a filter capacitor Full-wave Rectifier DC level can be improved to 100% of that obtained in HWR, by using the full-wave rectifier configuration shown. For t=0 T/2, D1 and D2 ON while D3, and D4 OFF. For t=t/2 T, D3, D4 ON, while D1 and D2 OFF. As seen form the waveform generated, the DC level for that configuration is twice that of the HWR. V dc(fwr) =2 V dc(hwr) = 2 0.318V s, ideal diode model. =2 0.318(V s -2V D0 ) simplified PIV rating >V s
Center Tapped Transformer FWR For t=0 T/2, D1 ON while D2, OFF. For t=t/2 T, D2 ON, while D1, OFF PIV rating >2V s Example 2.19 Clipper Circuits Clipper circuit is the circuit which clip off a portion of the input signal without distorting the remaining part of the signal Figure 3.33 Applying a sine wave to a limiter can result in clipping off its two peaks.
5.0V 0V -5.0V 0s 50ms 100ms 150ms 200ms 250ms 300ms V(R2:2) V(V1:+) Time Time Clippers Clipper circuits is used to remove one part of the signal without distorting the remaining part. The orientation of the diode determines the part of the signal that is removed, while the value of the DC controls the level of clipping. It is usually consists of, a diode, a resistance and a DC source. Clippers have two major configurations; Series Configuration, where the diode is connected in series with the the source. Parallel Configuration; where the diode is connected in parallel with the output port. Single Side Clippers Double Side Clippers Series Clippers 10V 0V -10V 0s 100ms 200ms 300ms 400ms V(Vs:+) V(RL:2) The output voltage is given by KVL as; v o = v s -V- V D such that the voltage at the diode input has to be greater than V T for the diode to conduct. Otherwise, the diode will be off and v o will be zero. Parallel Clippers Upper Side Clippers: 10V 0V -10V 0s 100ms 200ms 300ms 400ms 500ms V(V:+) V(RL:2) Time v 0 vi v D V Lower Side Clipper if if Dis OFF Dis ON 5.0V Double Side Clipper 0V -5.0V Lec(3-1) ٣٤ V(V10:+) V(V1:+) 0s 50ms 100ms 150ms 200ms 250ms Time
Clipper Circuits
Example:
Clampers A clamping circuit is the circuit that is used to clamp a signal to a certain DC level. It must contain a capacitor, a diode and a resistive element. The value of the discharging time constant of the capacitor, dis =RC>>T/2 has to be large enough to ensure that the capacitor doesn t discharge during the OFF period of the diode. The very small resistance of the diode R D makes the charging time constant ch =R D C so small that its can be considered that the diode charges in zero time. Clampers Rules: The Direction of the diode s arrow determines whether the signal is clamped up or down. The value of the DC source connected to the diode s anode determines the max or the min of the clamped signal respectively. Operation For t=0 T/2, D is ON Resistance R1 is short-circuited by the diode. C charges to V m in zero time (theoretically). For t=t/2 T,D is OFF. C discharges through R1 The Value of the output voltage is [V s (V m )+V c (V m )]
Clampers Rules: The Direction of the diode s arrow determines whether the signal is clamped up or down. The value of the DC source connected to the diode s anode determines the max or the min of the clamped signal respectively. Operation Example:
VOLTAGE MULTIPLIER CIRCUITS Voltage multiplier circuits are used to maintain low transformer peak voltage and stepping up the voltage to 2, 3,or 5 times this value Voltage Doubler ( Half-Wave) During +ive half cycle, D1 ON, D2 OFF, C1 charges to +V m During -ive half cycle, D1 OFF, D2 ON, C2 charges to +2V m as following; -V C2 +V c1 +V m =0 VC2=Vc1+V m =2V m
The Voltage Doublers Figure 3.38 Voltage doubler: (a) circuit; (b) waveform of the voltage across D 1. Dr. Mohamed Hassan Full-wave Voltage Multiplier During (+)ive half cycle, D1 ON, D2 OFF, C1 charges to +V m During (-)ive half cycle, D1 OFF, D2 ON, C2 charges to +V m. So the total output voltage applied to the load is 2V m.
Voltage Tripler and Quadrupler During (+)ive half cycle, D1 ON, C1 charges to V m. During (-)ive half cycle, D1 OFF, C2 charges to 2V m. through C1 and the secondary winding of transformer. During the next (+)ive half-cycle, D3 conducts, and C2 charges C3 to 2Vm Thank You