## Pi: 3.1415926535897932384626433…

Around 480, the Chinese mathematician Zu Chongzhi approximated a circle with a 12288 (212 x 3) sided polygon built by merely using a pile of wooden sticks called Counting rods, and derived what remained the most accurate approximations for π in the next 900 years: 3.1415926 < π < 3.1415927.

As simple as the shape of a harmonic circle could be, it’s key ratio number continues to be infinite and random till present ---- “reeks of mystery”.

To celebrate the beloved and mysterious number that captivated imaginations for thousands of year, March 14th has been established by math enthusiasts around the world as Pi Day, and it also happens to be Albert Einstein’s birthday. In my geek’s haven, we baked a chocolate cake with vanilla icing as a way to celebrate of God’s mathematical creation of π :-)

Designing any structure with cylindrical components involves π; for electrical engineers, it is about designing harmonic systems with harmonic signal chains. The invention of Laplace-domain enables us to view the continuous time-invariant system to the moments of harmonic vibration, and the key ingredient here is s = σ + 2 π f j. Derivatives and integrals in time domain (t) equate to multiply and divide in frequency domain (s); therefore analyzing the stability of system gets a lot easier by identifying the locations of zeros and poles in the s domain. For example, in the frequency domain, a four-pole band pass filter has the following frequency response, and the response for High and Low filter parts can be calculated by the formula below:

Depending on whether Lower or Higher filter parts are calculated, L or H indexes can be used in all formulas instead of X. Thanks to the PSoC switched capacitor block structure, the center frequency and Q (ratio of center frequency to bandwidth) are functions of the clock frequency and the ratios of the capacitor values chosen, and the center frequency can be set very accurately or adjusted by controlling the sample rate clock. And the maximum number of poles enabled by PSoC 1 family analog filtering is 8.

May the joys and wonders of π be with us forever :-)

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