If you purchase a new or used scope you will probably need a way to test its advertised bandwidth. One way to test the bandwidth of the scope is to feed a really fast pulse into the oscilloscope and measure its rise time. The reason why this makes sense is because a square wave contains many higher frequency harmonics. The frequency of its highest harmonic will determine the steepness of its falling or rising edge. If you look at a sinusoid wave of 1Ghz and one of 1Khz – the 1Ghz wave will have a steeper slope than the 1Khz sinusoid. A square wave or a pulse consists of the sum of many sinusoids, your scope bandwidth limitation will discard or attenuate the higher frequencies components and thus will alter the steepness of the wave that you see on your screen.
The bandwidth of the scope will be then given by the formula:
Bw = 0.35 / Tr (Note: 0.4 / Tr is sometimes used for modern digital scopes)
where Tr is the measured rise time of the pulse on the oscilloscope. This formula only stands when Tr >> Tra (Tr is much larger, usually at least 10 times than Tra) , where Tra is the actual rise time of the pulse. I will describe a quick circuit for building a fast pulse generator with a Tra of 50ps. 50ps corresponds to a bandwidth of 0.35/50ps = 7Ghz, so you should be safe to evaluate bandwidth of scopes up to 700Mhz. For scopes with larger bandwidths you can still use same method but you need to take into account Tra, the formula becomes then:
Bw = 0.35/SQRT(Tr^2 – Tra^2)
The circuit uses a single chip, ultra fast comparator ADCMP580 available from Analog Devices.
For this circuit you will need a dual rail power supply (+5/-5V) , if you don’t have one you can use an ATX power supply from a computer case – it has both +5V and –5V rails. You will also need a way to generate a (slow rising) input pulse that the circuit above will convert to a fast rising (50ps) pulse.
The input pulse must not exceed +3V/-2V according to ADCMP580 datasheet. Keep this in mind If you’re using your Arduino or a 555 timer circuit to feed in the input pulse , you will probably want to feed the pulse through a voltage divider if it exceeds these levels. Take into consideration that the ADCMP580 already has an internal 50Ohm resistor that you might use for your voltage divider. Also please note that if you signal goes only from 0V to 5V , Vn will need to be somewhere in-between, again you can form a voltage divider to set it at about 2.5V. The outputs Q/Qb will toggle when your signal crosses the threshold set by Vn. In my case since I have a pulse generator that feeds a pulse from –1.25V to 1.25V (2.5Vpp) I am setting my Vn threshold to ground. I am also using the internal 50Ohm termination just to place some “weight” on the circuit and filter out any noise pickup.
Rh is the hysteresis resistors this can be anywhere between 0 to 10Kohm. I found that a value of 100Ohm worked great for me . Let’s say your signal is going up but then because of the noise it decides to go a little down, hysteresis feature of ADCMP580 protects against the output reacting to that noise, the output signal will only go back down when the voltage will fall Vhys below the point that made it go up. Below is a chart that describes the relationship between Vhys and Rh. You can see that in my case since I am using a 100Ohm resistor I have about 55mV of a buffer zone, so my output will not fluctuate if the noise level is less than roughly 55mV, in other words it will always take more than 55mV change in signal to toggle the comparator back in opposite state.
The Build and Results
Luckily Analog Devices offers an inexpensive ADCMP580 demo board, I picked mine from Mouser for around 50 dollars. The board is basically a breakout of the ADCMP580 chip with some decoupling capacitors and 2.9mm connectors for signals and standard 4mm banana sockets for the power supplies. Fear not the 2.9mm connectors , they are generally compatible with SMA connectors so I used some SMA-M to BNC-M cables to connect the signals to my scope and signal generator. (Some people will warn you that if you have some very expensive equipment do not use SMA connectors with 2.9mm connectors – the tolerances might be different and you might break the connectors on your expensive equipment). I also used some 50Ohm SMA terminators, on the QB, LE and VN connectors. The schematic above calls for LE and VN to be connected to ground via wire, however I found that a 50Ohm cap did the job. In case of QB connector it must be terminated with 50Ohm to ground, even if you’re not using its output so the 50Ohm terminator is required. LEB is connected to VEE (-5V) via a 1Kohm resistor and you might notice in the picture I have a 100 ohm resistor in the HYS slot (see between the black Q and red VEE cable). You can see that the VTF_F, VTP_F, VTT, VCC0, CGND are left unconnected (the necessary connections are made by the blue jumpers on the board). Please note that although VCC1 may appear unconnected on the picture there’s an alligator clip under the board that connects it to the +5V rail of the power supply.
Once I completed the setup above I fed in a 2.5Vpp(@50Ohm load) 1Khz square wave into VP, my Q output was connected to my 500Mhz bandwidth oscilloscope, below is the result of this experiment:
The rise time of my input signal (Ch4) is 16.57ns while the rise time of the output (Ch1) is 536ps (average) with a dispersion of 36ps, the momentary reading when the screenshot was taken was 590ps. So let’s calculate the bandwidth of the scope, I am taking a conservative approach using the worst number of 590ps:
Bw = 0.35 / 590ps = 0.35 / (590* 10^-12) = 0.000593 * 10^12 Hz = 593 * 10^6 Hz = 593 Mhz
So my scope has a bandwidth of no less than 593Mhz on Channel 1. This is above it’s rated bandwidth of 500Mhz.
Conclusion and some notes
For around $50 I created a very fast pulse generator setup that allowed me to evaluate the bandwidth of my scope.
Please note that if you read the ADCMP580 datasheet you will find a Rise/Fall Time of 37ps, however this is the rise time from 20% to 80%, the scope measures the rise time from 10% to 90%. I simply prorated this number 37ps * (90-10) / (80-20) = 49.3ps ~ 50ps to get the rise time from 10% to 90%.
You will also see in datasheet the advertised equivalent rise time bandwidth of 8Ghz , I believe this comes from the formula 0.4/50ps = 8Ghz that applies to many modern digital scope. In my calculations I used the “old” conservative formula of 0.35/Tr instead of 0.4/Tr.
Finally please note that the output of ADCMP580 uses CML levels of 0V(High) and –0.4V(Low) according to datasheet. I found these levels to be actually lower in my setup (-0.472V High and -0.868V low), but with same difference of about 400mV as you can see in the scope screenshot below. If you have an explanation for this please leave a note in the comments section.
EVAL-ADCMP580BCPZ Evaluation Board
Evaluating Oscilloscope Bandwidths for Your Application
Digital Oscilloscope Bandwidth Measurement – direct and using risetime
Basics of Analog Oscilloscope Bandwidth
Analog Oscilloscope bandwidth considerations
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