Impulse Response of Digilent Analog Discovery Scope
Oct 17, 2012
The Analog Discovery
digital oscilloscope is specified as having an analog bandwidth of 5 MHz.
The measurement below demonstrates an "impulse" response measurement of this oscilloscope.
An optical impulse of ~ 35 ns was generated using a 2n2369a avalanche transistor pulsing a high-radiance infrared LED. The LED has a BW of ~ 25 MHz or a rise/fall time of ~ 15ns.
A moderate-speed photodiode receiver with a BW of ~ 14 MHz was used to detect the optical pulse. The diagram below shows the breadboarded receiver with Discovery
attachments for the scope inputs and the +/- 5V supply for the receiver op-amp. The photodiode was biased at -5V from the negative supply.
The infrared LED optical pulse circuit is also shown
(details of the optical pulse circuit are here).
The optical pulse response of the Discovery scope shows a reasonably clean shape with a fall time of ~ 30ns and minimal ringing. With such a clean response, it is quite possible to use
the low bandwidth Analog Discovery oscilloscope to measure the speed of light C, using a time-of-flight delay method with this simple gear.
To provide sufficient pulse separation for an accuract measurement of C, a delay path of about twice the full pulse width, or 100 ns (or 100' path-delay distance) is required which is easily
achieveable in a modest space, with some collimation optics for the diverging LED and a tilt mirror mount.
Alternatively, an inexpensive red diode laser, extracted from a laser pointer, will have sufficient modulation bandwidth to perform the same measurement, provided that
the pulse circuit is carefully adjusted to match the diode laser and prevent laser damage. The second response curve below is for a 2ns wide electrical pulse directly from an avalanche pulse circuit:
Response with photodiode amplifier and 30ns optical pulse:
Response with 2ns electrical pulse of amplitude ~ 5Vpeak:
Speed of Light Measurement
As an example, a red laser diode was used to measure the speed of light using the method described here. The laser was biased at a few mA
and a high-speed electrical pulse was AC coupled using a simple bias insertion circuit using an inductor to isolate the DC bias source. The arrangement is shown below:
The physical path difference between the two pulses was measured carefully with a tape measure to be 1458 +/- 12 cm (or 47' 10"). The optical pulse intensities from the two pulses as received by the photodiode were adjusted (using a simple mirror beam splitter)
to minimize any receiver/photodiode circuit nonlinearities due to pulse amplitude differences.
The first scope trace below shows the "shorter path" pulse from the beam-splitter, with the "long path" optical pulse blocked. The ~ 40ns width of the displayed pulse is limited
by a combination of the Discovery scope response and the photodiode op-amp circuit. The actual laser optical pulse-width is ~ 15ns :
The scope trace below shows both pulses detected simultaneously with the photodiode. The time difference was measured between the peaks of the pulses to be 49 +/- 2 ns:
With these measurements, the speed of light was determined to about 4% accuracy to be: (2.98 +/- 0.12)e10 cm/sec in good agreement with the accepted value of 2.99793e10 cm/sec.
The final scope trace below shows how the pulse separation can also be determined by measuring the "period" of the waveform (even though there are only 2 pulses, with a very low repetition rate
of ~ 100 kHz). In this case, the pulse amplitudes must be almost identical to avoid errors in the "period" measurement not representing the true pulse separation: