It’s worth mentioning that the meter readings in the above test will not
absolutely match the settings on the decade box. For instance, the 90
Ω
setting might read as 89.3 or 90.5 - very close to the ideal value, but not
perfect. There are a couple factors that contribute to this.
1. First, there is a tiny amount of intrinsic resistance in the circuit. The
leads of the multimeter, the traces of the PCB, and other components
are not ideal conductors, and exhibit a small amount of “parasitic
resistance.” In practice, it’s small enough to be negligible. If the all
zero setting is higher than an Ohm or two, doublecheck your work.
2. Second, the resistors in the decade resistance also have a small
amount of variability - they’re rated to be /- 1% of the given
value. There are 0.1% tolerance resistors, but they are significantly
more expensive than the 1% ones.
3. Third, the accuracy and precision of the multimeter itself will show
some variance.
How It Works
Resistors placed in series are additive. If we connect resistors end-to-end,
the overall resistance is the sum of the values. Below, we see that we can
make a 43K resistor by adding a 10K to a 33K.
The decade box employs this principle. Each decade is a string of the the
same value resistor. A rotary switch is used to select the point in the string
that corresponds to the desired value.
Each rotary switch has 10 positions, from 0 to 9. The 0 position simply
shorts the switch input to it’s output, and each successive position adds one
more resistor to the chain. A switch can go between 0 and 9 times the
decade value. If we need 10 times or greater the value, we move on to the
next decade.
The decades are arranged in series, as well. The tens control feeds the
hundreds control, and so on.
Constraints
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