1. 1 Passive components and circuits - CCP Lecture 4

2. /37 2 Content Basics  Circuit characteristics and parameters  Logarithmical representation Passive circuit elements  Resistor

3. /37 3 Circuit characteristics The transmittances of the electronic circuits are described by the linear or non-linear functions (for linear and non-linear circuits). The graphical representation of those functions is called electrical characteristic. In the case of linear circuits, they have linear segments representation.  By the graphical representation of a mathematical function which approximate the circuit operation  theoretical characteristics. (If those functions are approximated for simplification, they are called ideal characteristics).  By experimental measurements  experimental characteristics.

4. /37 4 Errors in determination of electrical characteristics In the case of theoretical characteristics:  The incapacity of the mathematical model to consider all factors which act over the circuit (sometimes, a simple model is used).  Approximations in solving of mathematical model (sometimes, the mathematical model is too difficult to be solved). In the case of experimental measurements:  The incapacity of total separation of interested quantities from others (noise).  Errors introduced by the measurements instruments and measurements method.

5. /37 5 Family of characteristics In most cases, an electric quantity is not dependent of a single variable (electric or non-electric variable). The dependency of a characteristic by the second (or even third) variable is represented as a family of characteristics in plane (or in space). In electronics circuit behavior, one of most important non-electric variable is the temperature.

6. /37 6 Family of characteristics - example a) Family of linear characteristicsb) Family of non-linear characteristics

7. /37 7 Circuit parameters The coordinates of some points from the electric characteristic are called circuit parameters. The parameters are chosen so that they emphasize the significant points on the characteristics (maximum and minimum, modulation points, etc.). If those points are referred to all the characteristics from a family, suggesting this way operation limits, the parameters are called limits parameters or limits values.

8. /37 8 Electronics data books They represent a collection of characteristics and parameters, made by the manufacturers, which describe the electronics components behavior. Usually, the data book characteristics and parameters have standardized signification => the signification is the same for all manufacturers.

9. /37 9 Classification of circuit characteristics and parameters Generally, the following characteristics and parameters regarding operation regimes, can be found in all data books:  Static (or DC) characteristics/parameters  Dynamics (or AC ) characteristics/parameters  Transient regime characteristics/parameters  Environment characteristics/parameters  Dissipated power characteristics/parameters

10. /37 10 DC Operation Regime In this operation regime, the electric quantities are not time dependent (during the observation period). These parameters reflect significant points of the characteristics or absolute limit values that cannot be exceeded.

11. /37 11 Alternating current (AC) operation regime The electrical stimulus applied to the circuit (component) are usually sinusoidal. In this case, the ratios (the transmittances) of output to input signals are called Gains (Amplifications) if they are greater than the unit value or Attenuations if they are smaller than the unit value. For an Amplifier Block the power amplification (power gain) Ap is defined as the ratio of output (load) power to input power.

12. /37 12 AC operation – frequency representation In alternative current, the transmittances are dependant by the signal frequency f, or the signal pulsation,  =2  f. The frequency dependency of transmittances is represented by the frequency characteristics. For frequency representation, the sinusoidal quantities are described like vectors: http://mathworld.wolfram.com/Phasor.html http://www.clarkson.edu/~svoboda/eta/phasors/MatchPhasors10.html http://www.physics.udel.edu/~watson/phys208/phasor-animation.html http://www-ccrma.stanford.edu/~jos/filters/Phasor_Notation.html http://www.usna.edu/MathDept/CDP/ComplexNum/Module_5/PhasorForm.htm

13. /37 13 Transfer function The ratio between two electric quantities represented by vectors is called transfer function. The transfer function is a complex quantity, characterized by the modulus and phase. Consequently, the frequency representation has two components:  Modulus-frequency characteristic (the amplitude ratio)  Phase-frequency characteristic

14. /37 14 The transient regime behavior The transient regime is an operation regime at a signal variation. The signal variation can be:  From a static value to another static value;  From a frequency value to another frequency value; In data-books this regime is described by time values such as: rising time, falling time, propagation time, etc. For example, if a power supply in a circuit is switched on there may be a surge, possibly with oscillations, before a steady flow of current is established. Circuits exhibit transients when they contain components that can store energy, such as capacitors and inductors.

15. /37 15 Environment effect over the circuits The environment acts over the electrical circuits through different factors. In the majority of situations, those factors have a disturbing effect on the circuit. The main environment factor affecting the electronic circuits is the temperature. Changes in the temperature affect the internal physical processes of the component (dimensions, chaotic thermal motion), changing its electrical characteristics. The temperature coefficients reflect the variation of different parameters:

16. /37 16 The dissipated power The electrical phenomena taking place in electronic devices and circuits are constantly affected by Joule effect (heat dissipation). The heat accumulation in the circuit structure will increase its temperature. Therefore, in data books are presented parameters and characteristics that restrict the dissipated power in the circuit under particular environment conditions. Not all the parameters specifying limit values are connected with the dissipated power; there are also other destructive phenomena.

17. /37 17 D.C. dissipated power Usually, the power is dissipated by a circuit regardless of the functioning regime: d.c., a.c., transient regime. Applying a constant voltage V R to a resistance R in d.c., the current will be: The power dissipated by the resistance will be:

18. /37 18 A.C. dissipated power Applying a sinusoidal voltage on a resistance: The current through the resistance will be: The instantaneous power dissipated by the resistance is: The average power dissipated:

19. /37 19 Tolerances of electrical parameters In data books, the parameters values indicated by the manufacturers are target values (nominal values). Due to a different number of factors (technological factors, reduced costs etc) the real values of the parameters are near to the rated (target) values. By the selective measurements, the manufacturers offers only those components which have the parameters in the some specific limits around the rated value. The maximum accepted difference between real and rated values is called tolerance.

20. /37 20 The tolerance expression The tolerance can be evaluate as absolute tolerance, specifying the minimum and maximum values of a parameter. The percentage tolerance reflects the maximum difference from a rated value. Knowing the percentage tolerance makes it easy to determine the absolute tolerance.

21. /37 21 Representation to a logarithmic scale By logarithmic scale representation, the x variable representation is replaced by the lgx (or lnx) representation. The logarithmic representation can be made only for positive values of a variable. In order to achieve this condition, the modulus representation of a variable is used.  By logarithm, the 0 value of axes became - .  The old smaller than unity values became negative, and greater than unity values became positive.

22. /37 22 Advantages of logarithmic technique  Allows a compression of representation domain.  Allows the obtainment of a linear characteristic.  Convert the multiplying/dividing operations in added/subtracting operation  these operations can be graphical performed.

23. /37 23 Linear representation - example The representation of the following complex functions. Representation of a 100Hz-100MHz frequency domain.

24. /37 24 Logarithmic representation- example The representation of the same values

25. /37 25 Characterization of electrical quantities by logarithmic ratio The transfer ratio represents the logarithms of a non-dimensional ratio (regarding the input and output). The transfer ratios are used to characterize the system transfer properties (ex: amplification, line attenuation etc).

26. /37 26 The double logarithmic representation - example The previous complex functions are used; The vertical axes is represented in dB (logarithmic scale); It can be observed the linear representation of these two functions.

27. /37 27 Bode diagrams representation The Bode diagram method assumes the replacement of the double logarithmic representation with asymptotes and tangents on the graphics. We obtain a graphical representation only with straight lines. This type of representation allows an easier additional graphical operation.

28. /37 28 Bode diagrams representation - example In this figure we added the Bode diagrams for the previous two functions:  Green for |A1 v |; Red for |A2 v |;

29. /37 29 Additional operation for Bode diagrams - example In the second figure we shown the amplification (with black- at the logarithmic scale, and with blue- by the Bode diagrams)

30. /37 30 Example 1 – Using Bode diagrams

31. /37 31 Example 2 – Using Bode diagrams

32. /37 32 Signals levels Absolute signal level report the system signal values to a fixed reference value. The relative level signal report the analyzed signal to an unknown value signal.  Voltage level-the reference value is V 0 =1  V  Current level-the reference value is I 0 =1  A  Power level- the reference value is P 0 =1pW

33. /37 33 Absolute levels in dB Observation 1 - knowing the absolute level makes it very easy to reconstruct the signal value: Observation 2- if the resistance R x, on which the signal is measured, is equal with the resistance R 0, on which the reference signal is measured, then the dB value of the power level is equal with the voltage and current levels

34. /37 34 Absolute levels in dB Observation 3 – if the power level in dB and the resistance value are known, the absolute voltage and current levels can be calculated in the following way: 3dB  2 1/2 6dB  2; 20dB  10; 120dB  10 6 Example – the following levels in dB have the corresponding values on linear scale:

35. /37 35 Absolute levels in Np If the decimal logarithms used for dB representation are replaced by natural logarithm, the levels will be evaluated in Nepers (Np). The relation between Np and dB and vice-versa are: 1Np  8,686dB, 1dB  0.115Np

36. /37 36 Operations with signal levels - example On a 50  resistor a V dB =120 dB  V level is measured. What is the absolute power level? And the level of current through the resistor? Method 1 Method 2

37. /37 37 Passive circuits elements Resistance as circuit element – Homework  Ohm’s Law  Power dissipated on a resistor In direct current In alternative current  Series and parallel connections  How resistance can limit the current?  How resistance can limit the voltage?