LC FILTERS

Introduction

This tutorial on LC filter design should allow you to incorporate into your radio design low pass, high pass and bandpass filters. Your electronic project should then hopefully perform the way you want it to.

Low pass and high pass filters are easy to design and implement. A high pass filter is really just the complement of a low pass filter. On the other hand bandpass filters can get quite complex. Also whilst a LC bandpass filter is particularly helpful in reducing image interference it is not the panacea for all ills. A properly designed, carefully constructed and aligned lc bandpass filter will give you a fractional bandwidth of about 2%. It is likely the percentage bandwidth might be somewhat worse than that.

Bandwiths of LC bandpass filters are more a function of the loaded Q of the circuit which in turn is determined by the terminating resistances. The shape factor i.e. - 6dB to - 60 dB points for LC bandpass filters is more a function of the number of resonators.

1. How this electronic tutorial is organised:

I would suggest you create a separate directory called lc-filters, perhaps with a sub-directory called tutorials.

Then I would advise you to save each LC filter lesson as you go. In this way if you wish to refer back later then you can. At times I will recommend you print directly from your online browser. This is because I have graphics files embedded throughout the lc filter lessons and these will not be saved with File|Save As|. The graphic files are to give you some schematics and also because some mathematical formula can't be readily inserted into the text.

Alternatively save the file and then right click to save any graphic you encounter to your new directory also.

2. Basis of the Tutorial

Clearly I must assume my reader will range from those who know nothing at all about LC filters - why else would you be here - to those who know just this and only that and then on up to those people who possibly know more than I do.

3. Tutorial Layout

I have endeavoued to provide sufficient hyperlinks to filter basics, low pass, high pass and bandpass filters so you can jump out if necessary and then come back to me. I have done some layout revision because it was pretty scatty - thanks to all those who continue to email constructive comments and suggestions.

Just follow the links forward and/or backward. Hopefully it will work. If it doesn't let me know because it is quite common for links to become corrupted over time..

4. Tutorial Quiz

I must assume my reader will be enthusiastic enough to want to do a few self-tests. You can look up the answers when you're finished.

5. L.C. Filter Tutorials

1. Basics you must learn to proceed further.

2. How low pass filters are designed - the basis of many other filters.

3. Again you could need a high pass filter in your application.

4. Down to a simple band pass filter for many purposes.

5. Next we have multi-pole narrow band pass filters.

6. How did they design I.F. Amplifier filters in the olden days anyway?

L/C FILTER DESIGN -

THE ANSWERS

Section 1 - Essential Basics of the Tutorial:-

1 (a). L/C - basics:-

1. What is the L/C for the following frequencies;
(a) 455Khz (b) 7224 Khz and (c) 9 Mhz.

Answers:(a) 122,354 (b) 485.38 and (c) 312.72

2. What capacitor will resonate at the above respective frequencies with the following respective inductors ;
(a) 679 uH (b) 22uH and (c) 3.81 uH.

Answers: (a) 180pF (b) 22pF and (c) 82pF

3. What is the resonant frequency for the following L/C (inductor - capacitor) combinations to the nearest Khz;
(a) 2,533,030 (b) 116,716 (c) 312.72 and (d) 2.53303.

Answers: (a) 100 Khz (b) 466 Khz (c) 9 Mhz and (d) 100 Mhz

Back to L/C .

1 (b). reactance - basics:-

1. What is the reactance of a 100pF capacitor at;
(a) 100Khz (b) 1.5 Mhz and (c) 22 Mhz.

Answers:(a) 15K915 ohms (b) 1K061 ohms and (c) 72R34ohms

Where K and R indicate the place of the comma or decimal point. Wait for a later tutorial to see my rabid tirade about the necessity for this method.

2. What is the reactance of a 22uH inductor at;
(a) 100Khz (b) 1.5 Mhz and (c) 22 Mhz.

Answers:(a) 13R823 ohms (b) 207R35 ohms and (c) 3K041 ohms

3. This is a revision of a previous tutorial:- What capacitor will resonate with the above inductor at;
(a) 7234Khz (b) 1224 Khz and (c) 3.5 Mhz.

Answers: (a) 22 pF (b) 769 pF and (c) 94 pF

Back to Reactance

1 (c). Q - basics:-

1. In our previous tutorial we calculated the reactance of a 22uH inductor at;
(a) 100Khz (b) 1.5 Mhz and (c) 22 Mhz.
What are the impedances if the unloaded Q's are respectively (a) 32, (b) 170, and (c) 110

Answers:(a) 442 ohms (b) 35K249 ohms and (c) 334K518 ohms

2. What is the effective r.f. resistance of the inductor above at the respective frequencies/Q.
(a) 100Khz/32, (b) 1.5 Mhz/170, and (c) 22 Mhz/110

Answers:(a) 0.432 or R432 ohms (b) 1R22 ohms and (c) 27R65 ohms

3. What is the correct method of describing the following resistances and capacitances.

(a) 0.68 ohms, (b) 10 ohms, (c) 220 ohms, (d) 1,800 ohms, (e) 82,000 ohms, (f) 470,000 ohms, (g) 5,600,000 ohms, and;

(h) 6.8 Pf, (i) 180 Pf, and (j) 4.7 uF

Answers:(a) R68 ohms (b) 10R ohms (c) 220R ohms (d) 1K8 ohms (e) 82K ohms (f) 470K ohms (g) 5M6 ohms (h) 6P8 (i) 180 Pf (j) 4U7