High Frequency signal with fast risetime, its bandwidth

[Geeniey]

Hi,

I am new to world of electronics and to high frequency Domain. But I am working on a design where I have a coax of 30cm length. I have used an external oscillator to generate 7GHz fast falling pulse. I am using a Controller to control the oscillator. Now I have a pulse of about 350ns Duration and 14ns rise time which travels down the coax.

The Information that I Need now is, what is the highest frequency component of this pulse and its bandwidth. How can I calculate this in real time?( I am using MPLAB IDE for this application.)

I would like to add new data Points between the sample Points of the Signal to increase the resolution. The Information that is measured is the reflection. (I have an ADC with 12 bit Resolution and 10Msamples/sec)

Can anyone help me in understanding how to build the algorithm for such numerical Approximation and Interpolation?

Your help will be greatly appreciated.

 

[f95toli]

The answer will depend on the exact shape of the pulse. If the pulse is really a trapezoid theoretically the answer is that the bandwidth is infinite.
However, in real applications one can often us the following rule of thumb: the bandwidth is given by 3/risetime; which in your case works out to be about 215 MHz.

I am not sure that I understand the rest of your question. What do you mean by "real-time"? Are you trying to use you ADC to characterize the shape of the pulse?
If so that won't work; at 10 MSa/s it is only going to be able to sample signals with a BW of about 5 MHz; nowhere near what you need.(it might be possible to build a "sampling" oscilloscope using an adjustable delay+extra electronics, but that would be very difficult, I have never actually seen anyone do that using a ADC)

 

[meBigGuy]

You need to understand the rough back of the envelope relationship between risetime and frequency. If you think of a sine wave, the fastest slope is at the zero crossing. It tends to be around 1/3 of the period. So, a risetime of 1ns implies a 333Mhz bandwidth.

An explanation here: http://www.edn.com/electronics-blog...-The-bandwidth-of-a-signal-from-its-rise-time

A more formal derivation here: http://en.wikipedia.org/wiki/Rise_time

 

[Geeniey]

The answer will depend on the exact shape of the pulse. If the pulse is really a trapezoid theoretically the answer is that the bandwidth is infinite.
However, in real applications one can often us the following rule of thumb: the bandwidth is given by 3/risetime; which in your case works out to be about 215 MHz.

I am not sure that I understand the rest of your question. What do you mean by "real-time"? Are you trying to use you ADC to characterize the shape of the pulse?
If so that won't work; at 10 MSa/s it is only going to be able to sample signals with a BW of about 5 MHz; nowhere near what you need.


(it might be possible to build a "sampling" oscilloscope using an adjustable delay+extra electronics, but that would be very difficult, I have never actually seen anyone do that using a ADC)

Sir,

Thank you for your Response!

I have a square waveform with 14ns rise time and 350ns Duration generated by a 7GHz Transistor which is controlled by a micro-controller. This is my incident pulse. The Information that I am interested in is the reflected pulse. This pulse is acquired from the coax after an mismatch has occured. This pulse is sent into a comparator which compares the PWM (with 50% duty cycle) of the incident with this reflected and generates a stop pulse.

This stop pulse is sent to a CTMU (Charge time measurement unit) of the micro-controller and the time is converted into a voltage. This voltage is given to ADC and the Output is viewed on the scope via UART.

Now, I want to view the Signal in high Resolution on the scope with more data Points to analyze the small reflections. So I am now struck where to start with and how can I do it !

Do I have to do FFT of the Signal? Or make Firmware changes like cascading the ADCs available. (the ADC used is 12 bit Resolution high Speed pipelined)

Since the Resolution depends on the rise time( which is the circuit Response to fast changing input), I must look for a way to improve the rise time. If the reflections are smaller than hte rise time, I cannot see them on the reflected Signal. I would like your suggestions on methods to achieve this.

I hope I made my preoblem clear now.

Your advice can help me improve my state of understanding of how to develop an algorithm to fulfil my requirement.

 

[Baluncore]

This is Time Domain Reflectometry. http://en.wikipedia.org/wiki/Time-domain_reflectometry

Your 10 MHz sample rate will limit you to about 100 feet resolution.

An alternative would be to transmit a linear RF chirp down the line, multiply the reflected signal by the transmitted chirp while continuously recording the A to D of the band limited product. Take the FFT of that trace and you will see spikes at frequencies that are reciprocals of the echo times. It works because the beat frequency between the TX and RX signals is proportional to chirp rate and distance to reflector.

 

[Geeniey]

Thank you Mr Baluncore for your advice.
Yes, it is Time Domain Reflectometry.
But I have a question regarding Transmitting Chirp down the transmitting line. In this process, the pulse is stretched. For example a 1ns pulse may be 1microsecond Long before it is upconverted and transmitted. This could possibly damage the rise time of the Signal. Where as for my apllication neds shorter rise time and lesser pulse width. So how can I solve this Situation?[/

 

[Baluncore]

We take advantage of the fact that the two signals, traveling in different directions on a linear transmission line are independent. With a step followed by a flat top, the step is fed through a series resistor with the same impedance as the line. Series R terminates the line to prevent multiple echoes, while providing the traditional TDR trace at the junction of the series resistor and the line.

With an RF chirp, it can be done in a number of ways. By using a directional coupler at the transmitter you can extract the generated TX chirp and the delayed reflected RX signals. The TX and RX signals are then multiplied by an RF mixer. There will be a DC offset determined by the couplers rejection. But the RX will be a different frequency from the present TX. The mixer produces a low frequency output that can be low pass filtered and then digitised at say 10 Msps. If the chirp lasts for 102.4 μsec there will be 1024 points of data available. The FFT of those 1024 points will give the spectrum of the beat between RX and TX. The frequencies present will be proportional to the return time via reflection from the impedance mismatch.

The FFT will give a conversion gain of √1024 = √ 2¹⁰ = 2⁵ = 32. That is a significant improvement over a sampled single step reflection.

The key to getting good results is to generate a chirp that is linear in kHz/μsec. If the chirp rate varies it is necessary to re-sample the digitised data to correct for the non-linearity on the time axis. By using a known good reference cable it is possible to characterise the chirp non-linearity by adjusting the timebase sample times to generate a clean sinewave.

 

[Geeniey]

Thank you Mr Baluncore!

I will work on it and get back to you.