# Using a slide rule to solve deciBel problems

Following a recent presentation on deciBels, it seemed appropriate to provide an example of how these problems with commonly solved before wide access to scientific calculators.

# Calculate Return Loss from measured 'Forward Power' and 'Reflected Power'

We measure 'Forward Power' at 125W, and 'Reflected Power' at 28W using a Bird 43 directional wattmeter. What is the Return Loss in dB?

So, we want to compute ReturnLoss=10*log(125/28).

In working with a slide rule, the slide rule is used to perform operations on normalised numbers and the exponents are calculated by mental arithmetic.

Since 1.25/2.8 will be less than one, we multiply 1.25 by the inverse of 2.8 and add subtract from the accumulated exponent so the slide stays on the right hand side of the stock.

(Shuffling the slide from side to side is a slow operation, and savvy users NEVER, well ALMOST NEVER shuffle the slide from side to side. There a a number of tricks that improved productivity by avoiding shuffling, and the technique above and the related dividing by the inverse for multiplication are the most commonly used ones.)

Fig 1 shows the first step, the start of the C scale is line up with 1.25 (being the 125W normalised, and carrying the exponent 2 in our head).

Fig 2 shows the next steps, slide the cursor to the point on the CI scale for 2.8 (the normalised value of 'Reflected Power'), the magenta highlight.  The distance from the start of the C scale to the cursor is proportional to the log of the product of 125 and 1/28, so we can look the common logarithm up where the cursor crosses the L scale and the figure is 0.6495, the cyan highlight.

The L scale value we have obtained is the mantissa of the logarithm, and the exponent due to 125, 28 and the inverse multiplication will be 2-1-1=0, so the complete logarithm is 0.6495. We now multiply that by 10 by shifting the decimal point one place to the right and round for a sensible precision for ReturnLoss=6.50dB.

Try solving the problem with a calculator and see how close the slide rule comes! The exact answer rounded to two decimal places is 6.50dB

You could of course perform 128/28 by long division for 4.46428571429..., if you quit at 4.464 (how long did that take?) and used 4 figure log tables for 4.46 you would get 0.649334... which you would multiply by 10 and round to 6.49dB.

Solving this problem takes less than 5s using a slide rule, about the same time with a scientific calculator, and several minutes with long division and log tables!

Yes, this is a problem that is very suited to slide rule solution.