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Get thousands of capacitance
values with this . . .
6-Decade Capacitance
Substitution BBox
ox
By NICHOLAS VINEN
When breadboarding or prototyping, sometimes you need to
experiment with a capacitor value. Substituting a range of different
capacitors can be a bit tedious. What you need is a capacitance
decade box, which makes it easy to find the right value for your
circuit.
O
UR 6-DECADE RESISTANCE
Substitution Box described in
April 2012 lets you easily find the
right value for a resistor in your circuit.
Sometimes though, you also need to
vary a capacitance. For example, you
may have an RC oscillator where the
resistor is integrated in an IC so you
can’t change it.
For whatever reason, when you need
to tune the value of a capacitor, this
84 Silicon Chip
new 6-Decade Capacitance Substitution Box is ideal. It gives you hundreds
of thousands of different capacitance
values to play with, from about 30pF to
6µF. It can be used to tune oscillators,
filters, time delays, compensation networks, rise and fall times, AC-coupling
stages, rail-splitters, feedback loops
and so on.
Even in situations where you can
calculate the required value of a ca-
pacitor, you may still need to tweak
it to work in a real circuit.
Design
A capacitance substitution box is
slightly trickier to design than a resistance substitution box. Because resistor
values sum when connected in series,
a rotary switch can be connected to a
resistor string giving you a variable
“tap” point. For example, with 10 x
siliconchip.com.au
6
S1b
4
3
9
100nF
1 F
1 F
4
5
100nF 100nF
2
150nF 150nF
180nF 220nF
100nF 180nF 220nF
3
S2
x100nF
8
1 F
6
1
10
1 F
3
S1a
1
12
1 F
2
x1 F
2
11
1 F
1
5
270nF 330nF
100nF 270nF 330nF
330nF 470nF
4
220nF 680nF
5
7
11
6
10nF
12
1
10
9
10nF
2
15nF
15nF
18nF
22nF
10nF
18nF
22nF
3
S3
x10nF
8
10nF
27nF
33nF
10nF
27nF
1nF
2.7nF 3.3nF
33nF
33nF
47nF
4
22nF
68nF
5
7
11
6
1nF
12
1
10
9
1nF
2
1.5nF 1.5nF
1.8nF 2.2nF
1nF
1.8nF 2.2nF
3
S4
x1nF
8
1nF
2.7nF 3.3nF
3.3nF 4.7nF
4
2.2nF 6.8nF
5
7
11
6
100pF
12
1
10
9
2
150pF 150pF
180pF 220pF
3
S5
x100pF
8
100pF 100pF
100pF 180pF 220pF 270pF 330pF
100pF 270pF 330pF
330pF 470pF
4
220pF 680pF
5
7
11
6
10pF
12
1
10
9
10pF
15pF 15pF
18pF
3
S6
x10pF
8
2
10pF
4
22pF
2.7pF 47pF
27pF
33pF
T2
2.2pF 68pF
33pF
47pF
22pF
68pF
5
7
6
T1
SC
2012
CAPACITANCE DECADE BOX
Fig.1: the circuit for the Capacitance Decade Box consists of just six rotary switches, two binding posts and a bunch
of different non-polarised capacitors. Sets of capacitors are paralleled to give the values required and switches S1-S6
select one set for each decade. The selected sets are connected in parallel, giving the required capacitance across
binding posts T1 and T2.
siliconchip.com.au
July 2012 85
18nF
22nF
10nF
18nF
15nF
15nF
27nF
68pF
100pF
100pF
270pF
180pF
100pF
220pF
180pF
S6
T2
10pF
10pF
10pF
x10pF
15pF
15pF
2.7pF
47pF
2.2nF
68pF
330pF
22pF
33pF
2.2pF
x100pF
1.5nF
33pF
270pF
150pF
47pF
100pF
220pF
1.8nF
100pF
330pF
1.5nF
2.2nF
1.8nF
x1nF
1nF
1nF
3.3nF
S5
470pF
1nF
2.7nF
1nF
T1
10nF
33nF
22nF
100nF
150nF
680pF
S4
3.3nF
x10nF
220pF
1nF
2.7nF
10nF
27nF
100nF
220nF
180nF
100nF
330nF
1 F
10nF
10nF
27pF
6.8nF
1 F
x100nF
270nF
2.2nF
3.3nF
1 F
4.7nF
1 F
1 F
180nF
x1 F
330nF
220nF
1 F
270nF
S3
33nF
33nF
S2
100nF
47nF
150nF
S1
Capacitance
Decade Box
© 2012
22nF
100nF
330nF
68nF
220nF
680nF
160140
1 204106121
470nF
18pF
22pF
Fig.2: follow this parts layout diagram to build the 6-Decade Capacitance Box. Note that the switches must be installed
with their anti-rotation spigots orientated as shown. The tops of these spigots must also be removed using side cutters.
100Ω resistors and an 11-position rotary switch, you can select a resistance
in the range of 0-1000Ω in 100Ω steps.
But connecting capacitors in series
gives a different result: two 100pF
capacitors in series gives 50pF, three
gives 33pF, four 25pF and so on. The
resulting values aren’t multiples of 10
and even if the values were convenient, there’s the additional problem that
the more capacitors you put in series,
the larger they need to be for the
whole string to have even a modest
capacitance.
So we need to connect capacitors in
parallel to make a substitution box. In
practice, this means we need 10 sets
of capacitors per decade, with values
of (for example) 100pF, 200pF, 300pF,
etc. Each switch selects one set for that
decade and the decades are wired in
parallel so that the capacitances combine. For example if you select 300pF
with one switch and 2nF with anoth
er, that will give you 300pF || 2nF =
2.3nF.
Because capacitor values are assigned logarithmically, to get decimal
values, we need one, two or three
capacitors in parallel. For example,
300pF can be made using two 150pF
capacitors while 400pF can be made
with 220pF and 180pF capacitors. We
have used values from the E6 series
where possible as these are the most
86 Silicon Chip
common ones. A few values from the
E12 series have also been used, where
necessary.
The result of all this is that you can
basically just “dial up” a value using
the six switches.
Circuit description
Stray capacitance
The full circuit is shown in Fig.1.
There is one rotary switch per decade,
labelled S1-S6. For the 10pF through
to 100nF decades they are single-pole,
10-position switches (S2-S6) while S1
has two poles and six positions.
All the capacitors in the circuit are
connected together at one end and to
binding post T1. Switches S1-S6 connect the other ends of the selected capacitors to T2 while the others remain
unconnected and so don’t contribute
to the total capacitance.
The capacitors around S2, S3, S4 and
S5 are arranged identically. The only
difference is in their values. The lowest
range (S6) is slightly different because
we can use two fewer capacitors since
we don’t worry about sub-picofarad
errors. S1 controls the 1µF range and
this is arranged a differently than the
others, to reduce the number of large
capacitors required.
It works the same way as the other
switches to select values up to 3µF.
For 4µF, the capacitors used for the
1µF and 3µF positions are connected
in parallel, using both switch poles.
Similarly, for 5µF, the capacitor sets for
2µF and 3µF are connected in parallel.
In an ideal world, the capacitance
you get would be exactly what you
have selected using S1-S6 but in reality, it will vary slightly, for a couple
of reasons.
The first is the stray capacitance of
the PCB itself which is around 30pF.
This adds to whatever capacitance
you have selected using the rotary
switches. It is irrelevant for large values but could be significant for values
below a couple of nanofarads.
The 10pF range is still useful, despite the fact that this stray capacitance
is so large in comparison. It means that
you can increase the capacitance in
small steps (~10pF). You just need to
remember to mentally add about 30pF
when selecting very small values.
Then there are the tolerances of the
capacitors themselves. 1% resistors
are commonly available and cheap but
a typical MKT or ceramic capacitor is
either ±10% or ±20%. For this project,
stick with the 10% types if possible.
Capacitor value variations are somewhat mitigated when paralleling similar values. Say we have two 1nF±10%
capacitors connected in parallel and
their errors are uncorrelated. Each
siliconchip.com.au
Parts List
1 PCB, code 04106121, 146 x
86mm
1 PCB, code 04106122, 157.5 x
95mm (front panel/lid) OR
1 front panel label
1 UB1 Jiffy box (Jaycar HB6011,
Altronics H0201)
1 2-pole 6-position rotary switch
(S1)
5 1-pole 12-position rotary
switches (S2-S6)
6 16-20mm knobs to suit S1-S6
(Jaycar HK7762, Altronics
H6042)
2 captive binding posts (Jaycar
PT0454, Altronics P9254)
capacitor will be between 0.9nF and
1.1nF, an error of ±0.1nF. While the
worst case values for the combination
are 1.8nF and 2.2nF, the average error
of any two capacitors is √(0.1nF2 +
0.1nF2) = 0.141nF or 7.07%.
If the capacitors are of the same
value and from the same batch, we
can’t assume the errors are uncorrelated. This effect is also less pronounced when the capacitor values
paralleled vary significantly. But given
the above, when we parallel multiple
capacitors of similar values, we can
generally expect slightly less variation
in the resulting capacitance than the
individual tolerances would suggest.
Using 10% capacitors, the result
will be accurate enough for most purposes but if you want better accuracy,
use capacitors with a tighter tolerance
(eg, 5%) or else buy several of each
and pick those closest to their nominal
values, using an accurate capacitance
meter. To be really tricky, where multiple capacitors are paralleled, you can
select them on the basis of the lowest
total error for each set.
Capacitor type
We use non-polarised capacitors in
this project to make it as versatile as
possible. MKT (metallised polyester)
types are used for values from 1nF up
to 680nF as they have good perforsiliconchip.com.au
mance, are commonly available and
have a consistently small size. Ceramic
capacitors are used for values below
1nF because they are more common at
these values. Those with an NP0/C0G
dielectric are better; these are common
for values of 100pF and below.
You can substitute different types if
you prefer, provided they fit.
The 1µF capacitors can be either
MKT or monolithic multilayer ceramic
(MMC). MKTs have better performance
and tend to have tighter tolerances but
cost more and some 1μF MKT capacitors may be too large (they need to have
a 5mm or 0.2-inch pin spacing).
Note that through-hole MKT and
MMC capacitors generally have a
voltage rating of at least 50V and this
should generally be sufficient.
Test leads
The most convenient way to use the
Capacitance Decade Box is to connect
it to your circuit with a short pair
of banana-plug-to-alligator-clip test
leads. But keep in mind that the leads
will have some capacitance which will
be added to that from the box itself.
Longer leads have more capacitance
so keep them short.
The leads also have some inductance (as does the PCB). In practice,
this limits the use of the box to circuits
operating at up to a few megahertz,
MKT Capacitors
6 1µF MKT or monolithic ceramic
(5mm lead spacing)
1 680nF
3 22nF
1 470nF
2 18nF
3 330nF
2 15nF
2 270nF
5 10nF
3 220nF
1 6.8nF
2 180nF
1 4.7nF
2 150nF
3 3.3nF
5 100nF
2 2.7nF
1 68nF
3 2.2nF
1 47nF
2 1.8nF
3 33nF
2 1.5nF
2 27nF
5 1nF
Ceramic Capacitors*
1 680pF
2 47pF
1 470pF
2 33pF
3 330pF
1 27pF
2 270pF
2 22pF
3 220pF
1 18pF
2 180pF
2 15pF
2 150pF
3 10pF
5 100pF
1 2.7pF
2 68pF
1 2.2pF
Note1*: C0G/NP0 ceramic
capacitors preferred
Note 2: the PCBs are available
from the SILICON CHIP Partshop
ie, it may not be suitable for use with
some RF circuits, mainly because of
stray capacitance.
Construction
The Capacitance Decade Box is
built on a 146 x 86mm PCB coded
04106121 which fits into a UB1 jiffy
box. Construction is easy; simply fit
the capacitors where shown on the
overlay diagram (Fig.2). Start with
July 2012 87
CONTROL
KNOB
BINDING POST
SWITCH
MOUNTING
NUT
BOX LID
STAR
WASHER
SWITCH
SHORTEN
PLASTIC
SPIGOT
BINDING POST
MOUNTING NUT
Fig.3: the PCB is
secured to the back
of the lid by resting
it on the tops of the
switches and doing
up the switch nuts.
The binding post
spigots are then
soldered to their
pads.
PCB
the lowest profile MKTs, then mount
the ceramic capacitors and the rest of
the MKTs.
Before fitting the switches, remove
the small plastic spigots that protrude
from the base using side-cutters (see
Fig.3). Clean up with a file, if necessary, then cut the shafts of all six
switches to a length of 10mm. This is
easily done by clamping the shaft in
a vice and cutting it with a hacksaw.
File off any burrs.
The switches can then be soldered to
the PCBs. Make sure the 2-pole switch
(S1) is fitted with the orientation
shown in Fig.2. All the switches must
be mounted flush with the PCB; check
before soldering more than two pins.
Housing
You can either drill the box lid and
attach a front panel label or else purchase a pre-drilled and screen printed
PCB which replaces the plastic lid
(157.5 x 95mm, coded 04106122).
This PCB lid gives your Capacitance
Decade Box a professional appearance
(the front-panel PCB is available from
the SILICON CHIP Partshop).
Alternatively, you can download
the front-panel label (in PDF format)
from the SILICON CHIP website, print
it out and use it as a drilling template
to make the eight holes in the plastic
lid. A second copy can then be printed
out, laminated and attached to the lid
using silicone adhesive.
Next, loosely fit the two binding
posts onto the lid, then remove the
nuts and washers from the rotary
switches. The lower washer has a locking pin and this is used to select the
number of switch positions available.
To do this, place the PCB flat on your
workbench, turn all the switches fully
anti-clockwise and insert the washers
for S2-S6 so that each locking pin goes
88 Silicon Chip
into the hole marked “10”. By contrast,
for switch S1, insert the locking pin
of the washer into the hole marked
“6”, so that it only rotates through six
positions.
That done, slip the star-washers over
the shafts, then push them through the
lid while keeping the PCB horizontal,
so you don’t knock the washers out
of alignment. Guide the binding post
shafts through the matching holes on
the PCB and then do up the six nuts
tight.
You can then tighten up the binding
post nuts using a small spanner and
after checking that they are correctly
aligned, solder them to the PCB pads.
Fit the knobs and then drop the lid
assembly into the box and attach it
using the four provided self-tapping
screws. If your box came with rubber
plugs that cover the screw holes and
you are not using the PCB lid, you can
fit them now.
Using it
As stated earlier, the Capacitance
Decade Box is most convenient in combination with short alligator clip leads
but you can also connect bare wires
into the binding posts, You can even
use solid-core wire so that the other
end can be plugged into a breadboard.
Keep in mind that the rotary switches will have either “make before break”
or “break before make” operation,
depending on the type supplied. This
means that if you change the capacitance while the unit is connected to a
working circuit, the capacitance will
briefly be either very low (~30pF) or
higher than usual while switching.
In most cases, this won’t upset the
circuit but it depends on its exact
configuration.
Once you have found the optimal
capacitance for your circuit using the
Capacitor Codes
Value
1µF
680nF
470nF
330nF
270nF
220nF
180nF
150nF
100nF
68nF
47nF
33nF
27nF
22nF
18nF
15nF
10nF
6.8nF
4.7nF
3.3nF
2.7nF
2.2nF
1.8nF
1.5nF
1nF
680pF
470pF
330pF
270pF
220pF
180pF
150pF
100pF
68pF
47pF
33pF
27pF
22pF
18pF
15pF
10pF
2.7pF
2.2pF
µF Value
1µF
0.68µF
0.47µF
0.33µF
0.27µF
0.22µF
0.18µF
0.15µF
0.1µF
.068µF
.047µF
.033µF
.027µF
.022µF
.018µF
.015µF
.01µF
.0068µF
.0047µF
.0033µF
.0027µF
.0022µF
.0018µF
.0015µF
.001µF
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
IEC Code
1u0
680n
470n
330n
270n
220n
180n
150n
100n
68n
47n
33n
27n
22n
18n
15n
10n
6n8
4n7
3n3
2n7
2n2
1n8
1n5
1n
680p
470p
330p
270p
220p
180p
150p
100p
68p
47p
33p
27p
22p
18p
15p
10p
2p7
2p2
EIA Code
105
684
474
334
274
224
184
154
104
683
473
333
273
223
183
153
103
682
472
332
272
222
182
152
102
681
471
331
271
221
181
151
101
68
47
33
27
22
18
15
10
2.7
2.2
decade box, you can disconnect the
it and measure the capacitance across
the output terminals. Alternatively,
you can just read out the position of the
switches, which should be accurate to
within a few percent of the true value
SC
for settings above 1nF.
siliconchip.com.au
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