LCS-1M - A Low-Cost Hobby Oscilloscope
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The signal input of the original LCS-1M design has an impedance of 133 kOhm. This is usually
sufficiently high to make signal aberrations due to the additional load negligible (e.g. with a 600 Ohm
audio source the 133 kOhm load introduces a level error of well under 1%; errors due to resistor
tolerances, power supply tolerances etc. add up to much more). But it precludes the usage of standard
1:10 scope probes, because these probes assume a scope impedance of 1 MOhm (they are basically
just 9 MOhm resistors, which then forms a 1:10 voltage divider with the scope input).
As already outlined in the design description the reason I had to choose a lower resistance is the input
capacitance of the op-amp (OP1 for scope channel 1). It is parallel to lower resistor (R12) of the input
divider, and at higher frequencies it shunts R12 and thus increases the division ratio (refer to
schematic page 5). That means higher frequencies get attenuated more - we got ourselves a low-pass
filter without even asking for one. Use a higher resistance divider and the problem only gets worse.
With a 1 MOhm divider I got a measly 60 kHz of bandwidth - too little to match the scopes 1 MS/s
sample rate. I needed to go down to these 133 kOhm to achieve around 400 kHz.
There is no way to get rid of this input capacitance. So "if you can't beat them, join them". If you add a
discrete capacitor C1 in parallel to R10 (the 100 kOhm resistor) you get a capacitive divider in parallel
to the resistive divider. If you choose C1 so that
R10 / R12 = Cin / C1 (Cin is OP1's input capacitance)
then the division ratios of capacitive and resistive divider are equal, and the division ratio is constant
over frequency - no more low-pass filter effect even though Cin is still there. (Actually the input
impedance decreases with frequency, but that's much less of a concern; the divider ratio does not
change).
Cin is usually not known very precisely (and will vary from device to device, even of the same type), so
scopes normally make C1 adjustable so you can trim it to optimum setting. Since I did not want
anything that need adjustment (because that tends to scare beginners off), I chose instead to also add
a capacitor (C4) in parallel to Cin - that way variations in Cin have much less effect.
Standard low-end scopes typically have an input capacitance of around 15pF, so was shooting for a
similar value. To get a 1 MOhm resistive with a ratio of 1:4, the resistors need to be 750 kOhm and 250
kOhm. As for the capacitors, after choosing C1 to be 18pF I varied C4 until I got the flattest frequency
response with a choice of 43pF. With that, the bandwidth doubles to around 1 MHz (not very important
given the scope's maximum sample rate), and the input impedance at DC is 1 MOhm, so you can now
use 1:10 probes to measure voltages higher than 20V!
Practical implementation:
To modify the LCS-1M with the new input stage you'll need to hack the board a bit - but it's pretty easy. If
you can't easly get the component value (750 kOhm, 250 kOhm, 43 pF and 18 pF) you can put them
together from two components each, combining them either in parallel or in series. Remember that for
resistors, the total resistance R_tot is
R_tot = R1 + R2 (series connection) or R_tot = (R1 * R2) / (R1 + R2) (parallel connection),
while for capacitors, the total capacitance C_tot is
C_tot = (C1 * C2) / (C1 + C2) (series connection) or C_tot = C1 + C2 (parallel connection).
For the resistors, as long as you get within about 1 - 2% of the goal, you are fine. The E24 series (1%
tolerance) has 750 kOhm and 249 kOhm available. Or with easier-to-obtain E12 series resistors (5%
tolerance) you can use 130+620 = 750, 270+470 = 740, or 330+430 = 760 (all series connected), or
two 1.5 MOhm resistors in parallel. For the 250 kOhm resistor use series combinations of 100K+150K,
30K+220K or 51K+200K.
The capacitors usually have larger tolerances anyway (5% or 10%), so don't get overly fussy here. If
43pF and 18pF aren't easily available, use 44pF (= two 22pF in parallel) and 20pF (= two 10pF in
parallel), or 47pF and 22pF. Alternatively, replace the 18 pF capacitor with a ~5 - 50pF trim capacitor,
measure a square wave and adjust it until it looks really square (no rounded edges and no overshoot
either).
Here are the updated schematics for the two channels:
sufficiently high to make signal aberrations due to the additional load negligible (e.g. with a 600 Ohm
audio source the 133 kOhm load introduces a level error of well under 1%; errors due to resistor
tolerances, power supply tolerances etc. add up to much more). But it precludes the usage of standard
1:10 scope probes, because these probes assume a scope impedance of 1 MOhm (they are basically
just 9 MOhm resistors, which then forms a 1:10 voltage divider with the scope input).
As already outlined in the design description the reason I had to choose a lower resistance is the input
capacitance of the op-amp (OP1 for scope channel 1). It is parallel to lower resistor (R12) of the input
divider, and at higher frequencies it shunts R12 and thus increases the division ratio (refer to
schematic page 5). That means higher frequencies get attenuated more - we got ourselves a low-pass
filter without even asking for one. Use a higher resistance divider and the problem only gets worse.
With a 1 MOhm divider I got a measly 60 kHz of bandwidth - too little to match the scopes 1 MS/s
sample rate. I needed to go down to these 133 kOhm to achieve around 400 kHz.
There is no way to get rid of this input capacitance. So "if you can't beat them, join them". If you add a
discrete capacitor C1 in parallel to R10 (the 100 kOhm resistor) you get a capacitive divider in parallel
to the resistive divider. If you choose C1 so that
R10 / R12 = Cin / C1 (Cin is OP1's input capacitance)
then the division ratios of capacitive and resistive divider are equal, and the division ratio is constant
over frequency - no more low-pass filter effect even though Cin is still there. (Actually the input
impedance decreases with frequency, but that's much less of a concern; the divider ratio does not
change).
Cin is usually not known very precisely (and will vary from device to device, even of the same type), so
scopes normally make C1 adjustable so you can trim it to optimum setting. Since I did not want
anything that need adjustment (because that tends to scare beginners off), I chose instead to also add
a capacitor (C4) in parallel to Cin - that way variations in Cin have much less effect.
Standard low-end scopes typically have an input capacitance of around 15pF, so was shooting for a
similar value. To get a 1 MOhm resistive with a ratio of 1:4, the resistors need to be 750 kOhm and 250
kOhm. As for the capacitors, after choosing C1 to be 18pF I varied C4 until I got the flattest frequency
response with a choice of 43pF. With that, the bandwidth doubles to around 1 MHz (not very important
given the scope's maximum sample rate), and the input impedance at DC is 1 MOhm, so you can now
use 1:10 probes to measure voltages higher than 20V!
Practical implementation:
To modify the LCS-1M with the new input stage you'll need to hack the board a bit - but it's pretty easy. If
you can't easly get the component value (750 kOhm, 250 kOhm, 43 pF and 18 pF) you can put them
together from two components each, combining them either in parallel or in series. Remember that for
resistors, the total resistance R_tot is
R_tot = R1 + R2 (series connection) or R_tot = (R1 * R2) / (R1 + R2) (parallel connection),
while for capacitors, the total capacitance C_tot is
C_tot = (C1 * C2) / (C1 + C2) (series connection) or C_tot = C1 + C2 (parallel connection).
For the resistors, as long as you get within about 1 - 2% of the goal, you are fine. The E24 series (1%
tolerance) has 750 kOhm and 249 kOhm available. Or with easier-to-obtain E12 series resistors (5%
tolerance) you can use 130+620 = 750, 270+470 = 740, or 330+430 = 760 (all series connected), or
two 1.5 MOhm resistors in parallel. For the 250 kOhm resistor use series combinations of 100K+150K,
30K+220K or 51K+200K.
The capacitors usually have larger tolerances anyway (5% or 10%), so don't get overly fussy here. If
43pF and 18pF aren't easily available, use 44pF (= two 22pF in parallel) and 20pF (= two 10pF in
parallel), or 47pF and 22pF. Alternatively, replace the 18 pF capacitor with a ~5 - 50pF trim capacitor,
measure a square wave and adjust it until it looks really square (no rounded edges and no overshoot
either).
Here are the updated schematics for the two channels:
Step-by-step instructions:
Channel 1:
Channel 2: same, only the part numbers change.
Channel 1:
- Unsolder R10 and R12.
- Replace R10 with a 750K resistor (R10 and R31 in the updated schematic) and 18pF capacitor
in parallel. Keep lead lengths short to reduce parasitic inductance. - Replace R12 with a 250K resistor and 43pF capacitor in parallel.
Channel 2: same, only the part numbers change.
- Unsolder R18 and R19.
- Replace R18 with a 750K resistor (R18 and R32 in the updated schematic) and 18pF capacitor
in parallel. - Replace R19 with a 250K resistor and 43pF capacitor in parallel.
Channel 1:
Channel 2:
