Electrical Circuits (2)

Transcription

1 Electrical Circuits () Lecture 4 Parallel Resonance and its Filters Dr.Eng. Basem ElHalawany

2 Parallel Resonance Circuit Ideal Circuits It is usually called tank circuit Practical Circuits Complex Coniguration v(t) R L L R C C Electric Circuits () - Basem ElHalawany

3 Ideal Parallel Resonance Circuit The total admittance Y Y Y Y3 Y R (jl) (-j/ C) - j Y jωc R ωl Y j( ωc / ωl) R Electric Circuits () - Basem ElHalawany 3

4 Ideal Parallel Resonance Circuit 4 At parallel resonance: At resonance, the admittance consists only conductance G = /R. The value o current will be minimum since the total admittance is minimum. The voltage and current are in phase (Power actor is unity). The inductor and capacitor reactances cancel, resulting in a circuit voltage simply determined by Ohm s law as: The requency response o the impedance o the parallel circuit is shown exactly opposite to that in series resonant circuits,

5 Ideal Parallel Resonance Circuit The Q o the parallel circuit is determined rom the deinition as 5 Reciprocal o series The current The currents through the inductor and the capacitor have the same magnitudes but are 8 out o phase. Notice that the magnitude o current in the reactive elements at resonance is Q times greater than the applied source current.

6 Ideal Parallel Resonance Circuit 6 Parallel resonant circuit has same parameters as the series resonant circuit. Resonance requency: ω p LC rad/s Hal-power requencies: Bandwidth and Q-actor:

7 Practical Parallel Resonance Circuit 7 The internal resistance o the coil must be taken into consideration because it is no longer be included in a simple series or parallel combination with the source resistance and any other resistance added or design purposes. Even though RL is usually relatively small in magnitude compared with other resistance and reactance levels o the network, it does have an important impact on the parallel resonant condition,. Find a parallel network equivalent to the series R-L branch

8 Practical Parallel Resonance Circuit 8 Redrawing the network

9 Practical Parallel Resonance Circuit 9 The resonant requency, p, can now be determined as ollows: Multiplying within the square-root sign by C/L and rearranging produces :

10 . Maximum impedance Practical Parallel Resonance Circuit At = p the input impedance o a parallel resonant circuit will be near its maximum value but not quite its maximum value due to the requency dependence o Rp. The requency at which maximum impedance will occur is:. Minimum impedance m is determined by dierentiating he general equation or ZT with respect to requency At = Hz, Xc is O.C, XL = zero As Rs is suiciently large or the current source (ideally ininity)

11 Practical Parallel Resonance Circuit The quality actor o the practical parallel resonant circuit determined by the ratio o the reactive power to the real power at resonance

12 Practical Parallel Resonance Circuit Bandwidth and Hal-Power point The cuto requencies and can be determined using the equivalent network shown in the igure:

13 Practical Parallel Resonance Circuit 3 The same eect as in series resonance

14 Assignment No() Validate your analysis using simulation (Proteus or Multisim) Hint (): review properties o resonant case to know how to validate the analysis using simulation Hint (): you may use current probe + Oscilloscope in Multisim Hint (3): you may use current probe + Mixed Graph in Proteus. Group solution is not permitted. Cheating or copying other students work will not be tolerated) Electrical Circuits () - Basem ElHalawany 4

15 Applications o Resonance Circuits 5 FILTER NETWORKS The ilter can be treated as a networks designed to have requency selective behavior A ilter can be used to limit the requency spectrum o a signal to some speciied band o requencies. Filters are the circuits used in radio and TV receivers to allow us to select one desired signal out o a multitude o broadcast signals in the environment. Passive ilter: it consists o only passive elements R, L, and C.. Active ilter: it consists o active elements (such as transistors and op amps) in addition to passive elements

16 Filter Networks 6 COMMON types o FILTERS Band-pass ilter Band-reject ilter Low-pass ilter High-pass ilter

17 Filter Networks 7 Important Table or determining the type o the ilter rom its Transer unction

18 8 Filter Networks Simple Passive band-pass ilter C L j R R V V H ) ( LC RC RC H H LC ) ( ) ( H H 4 / ) / ( L R L R LO LC 4 / ) / ( L R L R HI L R BW LO HI ) ( ) ( HI LO M H The RLC series resonant circuit provides a bandpass ilter when the output is taken o the resistor as shown in Fig. Transer Function

19 Simple Passive band-stop ilter Filter Networks 9 The RLC series resonant circuit provides a band-stop ilter when the output is taken o the LC as shown in Fig. A ilter that prevents a band o requencies between two designated values It is also known as a band-stop, band-reject, or notch ilter. BW = Bandwidth o rejection LC jl C at the capacitor acts as at the inductor acts as open circuit open circuit, are determined asin the band - pass ilter V V V V

20 High-Pass Filter Filter Networks At low requency the capacitor is an open circuit (Vo = ) At high requency the capacitor is a short and the inductor is open (Vo = Vin) Calculate/ Search or the transer unction?

21 Low-Pass Filter Filter Networks At low requency the capacitor is an open circuit (Vo = Vin) At high requency the capacitor is a short and the inductor is open (Vo = ) Calculate/ Search or the transer unction?

22 Filter Networks Band-Pass Filter (Using Parallel Resonance Circuits) Band-stop Filter (Using Parallel Resonance Circuits) Calculate/ Search or the transer unction?

23 Order o the Filter All the previously described iltered are Second Order Filters because they contain two reactive elements (L and C) It is possible to create another type o ilters using RC or RL only (First-order Filters) >>> not a complete series/parallel resonant circuit 3 Active Filters Passive ilters have several limitations:. Cannot generate gains greater than one. Loading eect makes them diicult to interconnect 3. Use o inductance makes them diicult to handle Using operational ampliiers one can design all basic ilters, and more, with only resistors and capacitors

24 Thank you 4

25 5 Filter Networks jq jq LC R L j RC j H LC R L j RC j C j L j R C j Z Z Z Z S S in out in in in C L R C out ) / ( ) ( V V V V V V Second Order Low-Pass Filter Transer Function (/)

26 6 Filter Networks Second Order Low-Pass Filter Transer Function (/) 9 Q Q H Q Tan Q Q jq jq H S s s S s s s in out V V