Discovering the effect measurement can have on a circuit
Further adventures in measuring the frequency of a tuned circuit
The vast majority of my projects to date have been microcontroller based and as a trainee with 2 years part time I still have a lot to learn. As I will be starting a HND in electrical and electronic engineering later this year I was keen to get experience in other areas of electronics.
In my last blog post looked at how to determine the resonant frequency of a tuned circuit, calculating and measuring this. The calculated and measured figures didn't quite match up and it was clear something wasn't quite right.
Initially the reason why the measured and calculated results differed so much wasn’t clear, so I began looking for possible explanations as to what could have affected my results.
I received a comment on the post which explained how each of the oscilloscope probes have a capacitance of their own, and how this was effectively across GND and the measurement pin, so would end up in parallel with the variable capacitor. They went on to explain how the stray oscilloscope capacitance would explain the results shown in my graph, as the additional capacitance displays a much more noticeable effect when the capacitor under test is set to a small value.
Suddenly everything made sense; when I initially made the calculations I hadn't taken into account any other capacitance in the circuit other than that of the variable capacitor!!
In their comment they also explained that if I removed the capacitor under test I would be able to find the resonant peak and work out a capacitance value which should correspond to that of the oscilloscope probe in parallel with the coils own residual capacitance.
Factoring in the capacitance of the probes
I then began trying to find the specified capacitance of each probe in their manufacturers data sheets. I managed to find this for one of the probes (grey) but not the other. I decided to measure the capacitance of the grey probe with an LCR meter and then compare it with the value stated in the specifications. Upon comparison I found that these values were very close, so I decided it would be reliable enough to measure the capacitance of the other (black) probe and then use these measurements for calculating the resonant frequency.
As the probes attach to the circuit in parallel the capacitances add, and these were added to that of the capacitor.
I then substituted the values in to the formula f= 1/(2Pi Root LC) to achieve a new set of calculated results:
Based on the results shown above, overall the new calculations do sit closer to the actual results. However they do not sit as close to the measured results as I would have liked.
Working in reverse
To verify the capacitance of the probes and to ensure the measurements and calculations were correct I decided to work in reverse. This time I measured the resonant frequency without a capacitor in circuit. The capacitance then calculated from this should theoretically match up with the sum of the measured capacitance of each of the probes plus the residual capacitance of the circuit.
I set this up the same as I did previously, but this time I used a smaller breadboard, less wires and arranged it much neater in the hope this would minimise any additional capacitance/inductance in the circuit.
To calculate the results I transposed the formula F=1/2Pi(root LC) to make 'C' the subject which looks like this: C=1/(2PiF)^2 L
Below are the results obtained from these measurements and calculations.
The above results show pretty much what I would have expected: The measured resonant frequency is very similar to what it was when I measured it with the variable capacitor when open. I believe this is because when the capacitor was fully open there was very little capacitance at all, so this explains the small difference.
These results also show that using this method of calculation there is very little difference between the calculated capacitance of the overall circuit for when both long wave and medium wave were tested. However, the calculated capacitance and measured capacitance are still quite a way off each other, with a difference of between 104.5pf and 112.9pf. This lower value (calculated from the resonant frequency) in the overall circuit suggested to me that there may be additional inductance throwing off the expected results. For example, the inductance of the coils may be higher than measured or something else may be having an effect.
What do the results show?
It's important to note that the measurements haven’t been like for like: initially the capacitance was measured of just the probes, then the capacitance was calculated for the whole circuit – we are not comparing the same thing.
Next time I work with an analogue circuit I will be sure to take into account the capacitance of all the components, and as suggested draw out an equivalent circuit for the whole system. I also have to bear in mind that measuring a circuit can have a significant impact on it's performance; by attaching probes this introduces extra capacitance which can affect measurements greatly.
Thanks to “takemetuit1” for their comment on my previous post, it has been a great help and is much appreciated!
CommentsAdd a comment
Measuring an open coil with a ferrite rod antenna nucleus over a table is just "calling" for trouble. Noise is the first one.
Nearby conductors also can decrease effective inductance, even a wood surface could have a not predictable effect.
If I had to measure this setup anyway, I will use a small loop probe instead of connecting an oscilloscope probe in parallel with the tank circuit.
If the loop is not feasible I will split the tuning C in two; one close to tune the circuit and other in series ten or more times the first one.
If by no means I have to use a probe, then it should be a 100:1 low capacitance one.
Maybe I am too old, but what comes to my mind is a "grid dip meter" for such measurement.
Both ways interaction between measurement and object measured is minimized.
On the other hand you have to be aware that every measurement changes what we measure.
On the limit the Heisenberg's uncertainty principle of quantum physics applies.
My two cents