1. Lesson 24: Introduction to Filters

2. 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.

3. 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…

4. Filters Some Types: Some terms:
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.
Stop Band
Pass Band
Some terms:
Stop Band – are the frequencies that are rejected.
Pass Band – are the frequencies which are accepted into the system.

5. 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 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

6. 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 level.

7. 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.
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.
To summarize, the magnitude of the ratio of Vo to Vi can be found by:

8. 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 level.

9. 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.
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.
To summarize, the magnitude of the ratio of Vo to Vi can be found by:

10. 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:
Where τ is the time constant we discussed in RC and RL circuits:
Therefore, to find the cutoff frequency:

11. 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.

12. 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.

13. Radio Spectrum
The primary frequencies used in the Navy are:

14. 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.

15. QUESTIONS?