Presentation on theme: "Frequency Characteristics of AC Circuits"— Presentation transcript:
1 Frequency Characteristics of AC Circuits IntroductionA High-Pass RC NetworkA Low-Pass RC NetworkA Low-Pass RL NetworkA High-Pass RL NetworkA Comparison of RC and RL NetworksBode DiagramsCombining the Effects of Several StagesRLC Circuits and Resonance
2 IntroductionFilters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies outside this band. This property of filters is also called “frequency selectivity”.Filter can be passive or active filter.Passive filters: The circuits built using RC, RL, or RLC circuits.Active filters : The circuits that employ one or moreop-amps in the design an addition toresistors and capacitors
3 Advantages of Active Filters over Passive Filters Active filters can be designed to provide required gain, and hence no attenuation as in the case of passive filtersNo loading problem, because of high input resistance and low output resistance of op-amp.Active Filters are cost effective as a wide variety of economical op-amps are available.
4 ApplicationsActive filters are mainly used in communication and signal processing circuits.They are also employed in a wide range of applications such as entertainment, medical electronics, etc.
5 Earlier we looked at the bandwidth and frequency response of amplifiers Having now looked at the AC behaviour of components we can consider these in more detailThe reactance of both inductors and capacitance is frequency dependent and we know that
6 We will start by considering very simple circuits Consider the potential divider shown herefrom our earlier consideration of the circuitrearranging, the gain of the circuit isthis is also called the transfer function of the circuit
7 A High-Pass RC Network Consider the following circuit which is shown re-drawn in a more usual form
8 Clearly the transfer function is At high frequencies is large, voltage gain 1At low frequencies is small, voltage gain 0
9 Since the denominator has real and imaginary parts, the magnitude of the voltage gain is WhenThis is a halving of power, or a fall in gain of 3 dB
10 The half power point is the cut-off frequency of the circuit the angular frequency C at which this occurs is given bywhere is the time constant of the CR network.Also
11 Substituting =2f and CR = 1/ 2fC in the earlier equation gives This is the general form of the gain of the circuitIt is clear that both the magnitude of the gain and the phase angle vary with frequency
12 Consider the behaviour of the circuit at different frequencies: When f >> fcfc/f << 1, the voltage gain 1When f = fcWhen f << fc
13 The behaviour in these three regions can be illustrated using phasor diagrams At low frequencies the gain is linearly related to frequency.It falls at -6dB/octave (- 20dB/decade)
14 Frequency response of the high-pass network the gain response has two asymptotes that meet at the cut-off frequencyfigures of this form are called Bode diagrams
15 High-Pass Filter Response A high-pass filter is a filter that significantly attenuates or rejects all frequencies below fc and passes all frequencies above fc.The passband of a high-pass filter is all frequencies above the critical frequency.VoActual responseIdeal responseIdeally, the response rises abruptly at the critical frequency, fL
16 The critical frequency of a high-pass RC filter occurs when XC = R and can be calculated using the formula below:
17 A Low-Pass RC Network Transposing the C and R gives At high frequencies is large, voltage gain 0At low frequencies is small, voltage gain 1
18 A Low-Pass RC Network A similar analysis to before gives Therefore when, when CR = 1Which is the cut-off frequency
19 Therefore the angular frequency C at which this occurs is given by where is the time constant of the CR network, and as before
20 Substituting =2f and CR = 1/ 2fC in the earlier equation gives This is similar, but not the same, as the transfer function for the high-pass network
21 Consider the behaviour of this circuit at different frequencies: When f << fcf/fc << 1, the voltage gain 1When f = fcWhen f >> fc
22 The behaviour in these three regions can again be illustrated using phasor diagrams At high frequencies the gain is linearly related to frequency. It falls at 6dB/octave (20dB/decade)
23 Frequency response of the low-pass network the gain response has two asymptotes that meet at the cut-off frequencyyou might like to compare this with the Bode Diagram for a high-pass network
24 BASIC FILTER RESPONSES Low-Pass Filter ResponseA low-pass filter is a filter that passes frequencies from 0Hz to critical frequency, fc and significantly attenuates all other frequencies.roll-off rateVoActual responseIdeal responseIdeally, the response drops abruptly at the critical frequency, fH
25 Transition region shows the area where the fall-off occurs. Passband of a filter is the range of frequencies that are allowed to pass through the filter with minimum attenuation (usually defined as less than -3 dB of attenuation).Transition region shows the area where the fall-off occurs.roll-off rateStopband is the range of frequencies that have the most attenuation.Critical frequency, fc, (also called the cutoff frequency) defines the end of the passband and normally specified at the point where the response drops – 3 dB (70.7%) from the passband response.
26 VoAt low frequencies, XC is very high and the capacitor circuit can be considered as open circuit. Under this condition, Vo = Vin or AV = 1 (unity).At very high frequencies, XC is very low and the Vo is small as compared with Vin. Hence the gain falls and drops off gradually as the frequency is increased.
27 The bandwidth of an ideal low-pass filter is equal to fc: The critical frequency of a low-pass RC filter occurs whenXC = R and can be calculated using the formula below:
28 A Low-Pass RL NetworkLow-pass networks can also be produced using RL circuitsthese behave similarly to the corresponding CR circuitthe voltage gain isthe cut-off frequency is
29 A High-Pass RL NetworkHigh-pass networks can also be produced using RL circuitsthese behave similarly to the corresponding CR circuitthe voltage gain isthe cut-off frequency is
30 A Comparison of RC and RL Networks Circuits using RC and RL techniques have similar characteristics
34 Multiple high- and low-pass elements may also be combined
35 RLC Circuits and Resonance Series RLC circuitsthe impedance is given byif the magnitude of the reactance of the inductor and capacitor are equal, the imaginary part is zero, and the impedance is simply Rthis occurs when
36 Resonant frequency This situation is referred to as resonance the frequency at which is occurs is the resonant frequencyin the series resonant circuit, the impedance is at a minimum at resonancethe current is at a maximum at resonance
37 The quality factor, QThe resonant effect can be quantified by the quality factor, Qquality factor, Q: is the ratio of the energy dissipated to the energy stored in each cycleit can be shown thatand
38 RLC circuit is an acceptor circuit The series RLC circuit is an acceptor circuitthe narrowness of bandwidth is determined by the Qcombining this equation with the earlier one gives
39 SUMMARYThe bandwidth of a low-pass filter is the same as the upper critical frequency.The bandwidth of a high-pass filter extends from the lower critical frequency up to the inherent limits of the circuit.The band-pass passes frequencies between the lower critical frequency and the upper critical frequency.A band-stop filter rejects frequencies within the upper critical frequency and upper critical frequency.
40 Passive Analog Filters Background:Four types of filters - “Ideal”lowpasshighpassbandpassbandstop
41 Passive Analog Filters Background:Realistic Filters:lowpasshighpassbandpassbandstop