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Lesson 24: Introduction to Filters 1 Learning Objectives • • • Become familiar with the frequency response of high-pass and low-pass filters. Learn to calculate the cutoff frequency and describe the phase response. Be able to calculate the cutoff frequencies and sketch the frequency response of a pass-band or stop-band filter. Develop skills in interpreting and establishing the frequency response of any filter. 2 Filters Introduction • Filters are used extensively in communications applications to either select a particular frequency of interest or to ignore (reject) frequencies that may be interfering with your equipment. • As the image of the antennas on the ship shows there are many opportunities for interference to occur during the transmitting and receiving of signals. • This is where the filter comes in… 3 Filters • Some Types: • Passive filters are those filters composed of series or parallel combinations of R, L, and C elements. • Low-Pass • High-Pass • Band-Pass • Band-Stop • Active filters are filters that employ active devices such as transistors and operational amplifiers in combination with R, L, and C elements. • Some terms: • • Stop Band – are the frequencies that are rejected. Pass Band – are the frequencies which are accepted into the system. Stop Band 4 Pass Band Filters • Any frequency in the pass band will ‘pass’ through to the next stage of the circuit with at least 70.7% of the maximum output voltage. • Recall the use of the 0.707 level to define the bandwidth of a series or parallel resonant circuit (both with the general shape of the pass-band filter). Stop Band Pass Band 5 Low-Pass Filter • Again, as the name would indicate, a low-pass filter (LPF) will allow signals of some lower desired frequency to ‘pass’ into the circuit, but at the same time it rejects frequencies above the cutoff frequency. • The cutoff frequency is that point at which higher frequencies are rejected. Av is the normalized value of the ratio of Vo / Vi. The maximum value of Av is 1 and the cutoff frequency is defined at the 0.707 level. 6 Low-Pass Filter • At very high frequencies the reactance (Xc) of the capacitor is very small (and thus acts like a short) and can be it can be shown that Vo = 0V in this case. X C f HighH z • At very low frequencies the reactance (Xc) of the capacitor is very large (thus acts like an open) and it can be shown that Vo = Vi in this case. X C f 0 H z • 1 0 2 fC 1 2 fC To summarize, the magnitude of the ratio of Vo to Vi can be found by: 7 High-Pass Filter • A high-pass filter (HPF) allows signals of some higher desired frequency to ‘pass’ into the circuit, but at the same time it rejects frequencies below the cutoff frequency. • The cutoff frequency is that point at which lower frequencies are rejected. RC High-Pass Filter Av is the normalized value of the ratio of Vo / Vi. The maximum value of Av is 1 and the cutoff frequency is defined at the 0.707 level. 8 High-Pass Filter • At very high frequencies the reactance (Xc) of the capacitor is very small (and thus acts like a short) and can be it can be shown that Vo = Vi in this case. X C f HighH z • 1 0 2 fC At very low frequencies the reactance (Xc) of the capacitor is very large (thus acts like an open) and it can be shown that Vo = 0 in this case. X C f 0 H z • 1 2 fC To summarize, the magnitude of the ratio of Vo to Vi can be found by: 9 Basic Low and High Pass Filter Design • For both a low pass and high pass filter response we can find the inflection point called the cutoff frequency which is simply: 1 fc 2 * • Where τ is the time constant we discussed in RC and RL circuits: R *C • Therefore, to find the cutoff frequency: 1 fc 2 * RC 10 Band-Pass Filter • As the name would indicate, a band-pass filter (BPF) will allow signals of a desired frequency to ‘pass’ into the circuit, but at the same time it rejects all other unwanted frequencies. • The last lesson showed us that a series resonant circuit has a frequency response characteristic similar to the one appearing in the figure below. 11 Band-Stop Filter • The band-stop filter will reject signals of some specified bandwidth (i.e. frequency range) from entering the circuit. • ALL other frequencies (not within the specified bandwidth) are accepted. • Also known as a notch filter because it ‘notches out’ (rejects) a specific frequency. 12 Radio Spectrum • The primary frequencies used in the Navy are: 13 Example Problem 1 Design an RC Low Pass Filter for the HF band (3-30MHz) using a resistor value of 5Ω. Draw the circuit and label the frequency response curve. From the problem statement we know that our cutoff frequency (fc) is 30MHz and the R=5 Ω. 1 , R *C fc 2 * 1 2 * R * C 1 1 C 1.06nF 2 * R * f c 2 *5 *30 MHz fc R 5 C 1.06nF 14 30MHz QUESTIONS? 15