Calculating modulation index

[dylancor]

Hello,

I am trying to calculate the modulation index and display it on my front panel. 

B = standard deviation / carrier freqency

Does anybody have an example of this or insight on the best approach to take?

Cheers,

Dylan

[johnsold]

Dylan,

I do not see anything which looks like frequency modulation in the VI you posted. 

What information do you have and what are you trying to measure or analyze?

Lynn

[dylancor]

Hello Lynn,

I am building a spectrum analyzer. My labview VI will read the voltage coming from my hardware components using the ADC on the my daq device. each voltage reading represents a distinct signal power being read. The my daq is also generating a ramp signal with the block labelled generate ramp in my VI. The voltage on the ramp determines what frequency I am reading. 

Essentially, I will be given a signal between -20 and -60 dbm at a frequency between 50 - 54 Mhz. This is the input which I need to find the modulation index of.

Dylan

[johnsold]

Dylan,

So, you are trying to determine the modulation index from the spectrum.

The reverse problem is somewhat easier. It can be calculated analytically. I would start by determining what the spectrum looks like as a function of modulation index. Then try to see how you can get what you want from the spectrum.

Will you be using the NI myDAQ ADC? It has a maximum sampling rate of 200 kHz. On the +/-2 V range the resolution is 61 uV. Your signal is 50 MHz, or 250 times higher than the maximum sampling frequency.  A 0 dBm signal (1 mW into 50 ohms) is 224 mV rms. The largest signal you expect at -20 dBm is 2.2 mV. At -60 dBm the signal is 0.22 uV.  The largest of your signals is only ~36 LSB. The smallest signal is way below the threshold of your ADC.  That device cannot even begin to convert your signal.

Lynn

[dylancor]

Lynn,

Yes I will be using the NI myDAQ ADC. My hardware components take care of the signal strength and frequency problems.

I am just unsure how to measure the standard deviation from this signal.

Dylan

[johnsold]

Dylan,

Standard deviation is a statistical measure. Deviation in a frequency modulation system is something completely different. It is the change of frequency from the carrier frequency at the peak voltage input to the modulator.  For example if a 50 MHz carrier hits a frequency of 50.001 000 MHz (50 MHz plus 1 kHz) at the peak input to the modulator, then the deviation is 1 kHz.  Assuming a symmetrical modulation with a sinusoidal signal the instantaneous frequency would be 49.999 000 MHz at the negative peak.

The spectrum is not simply carrier frequency +/- deviation. Model the signal as sin(2*pi*[Fc+ M*sin(2*pi*Fm*t)]*t), where Fc is the carrier frequency, Fm is the modulation frequency, and M is the deviation*). Now, calculate the Fourier transform of that signal. If I recall correctly, the spectrum includes Bessel functions. 

* This may not be the standard definition of deviation. I am writing from memory and have not worked with these equations for 30 years.

What kind of hardware components will you have between the rf signal and the myDAQ? Will they preserve the spectrum?

Lynn

[dylancor]

Lynn,

Thank you for you insight. I will model the signal with the equation you have given me.

As far as my hardware components, I am mixing the signal with a voltage controlled oscillator. With this new signal I pass it through a series of amplification stages, crystal bandwidth filter, find the peak voltage and then read it with the myDAQ device. I have tried to conserve the intial signal as close to as possible, but I believe the phase becomes distorted through the amplifiers.

Dylan

[johnsold]

Dylan,

Please do a little research.  Look up FM in any textbook on communication theory to confirm the form of the equation.

What is frequency is your IF amplifier and crystal filter?

Lynn