Amplifier & Filter

Emporium

The amplifier and filter section is an op-amp network called a leapfrog bandpass filter that amplifies audio frequencies in the 440 Hz region.  The resistors and smaller capacitors determine three important values: the center frequency, 440 Hz = 1 / (2p × 110kW × 3300 pF), the “Q” (quality factor), 10 = 10M / 1M, and the gain, 100 = 10M / 100k .  The gain depends on the 100k resistor at the input.  The other 100k resistors are noncritical but should be the same value.  The 3300 pF capacitors should be 5% tolerance.  These are harder to get, but so long as 440 Hz = 1 / (2p × R × C), that is, 0.00036 = R × C another resistor/capacitor combination can be substituted.  Remember, you need two of each.

A signal near 440 Hz (the center frequency) will be amplified by a factor 100 (the gain).  The gain depends on all the earlier components and its purpose is to get enough signal to the LM567 in the frequency detector section.  The bandwidth is 44 Hz, which is 440 Hz (the center frequency) divided by 10 (Q, the quality factor).  The only frequencies appreciably amplified are those in this band, 418 - 462 Hz, in other words, 440 Hz ± 5%.  Since the components that determine the center frequency are 5% tolerance, a Q of 10 is as high as it can be without risking that the filter rejects the intended frequency because the components were out of tolerance.

This design comes from the book by Horowitz and Hill titled The Art of Electronics (1989), Figure 5.19.  The design is both over my head and easy to use, and makes good use of one good IC.  The LM324 is easy to get and needs only a 5V supply.  For the op-amps in this circuit, the reference voltage is 2.5 V.  The four op-amps are interchangeable.