frequency modulation direct method
Frequency Modulation
Xavier University – Ateneo de Cagayan
Submitted by: Submitted to:
Dapal, Jamie Daisylette Engr. Mary Jean Apor
Fermano, Jerick James
Oraiz, Gerard James
Sabunod, Shane John
Siman, Lester C.
Objectives:
1. To obtain a frequency modulated signal via direct method
2. To understand the process of frequency modulation by direct method
Background Theory: Frequency modulation uses the information signal, Vm(t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:
Information: Vm(t)
Carrier: Vc(t) = Vco sin ( 2 fc t +
FM: VFM (t) = Vco sin (2 fc + (f/Vmo) Vm (t)t +
We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: f, the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: fc + (f/Vmo) Vm (t) now varies between the extremes of fc - f and fc + f. The interpretation of f becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency.
We can also define a modulation index for FM, analogous to AM:
= f/fm , where fm is the maximum modulating frequency used.
The simplest interpretation of the modulation index, is as a measure of the peak frequency deviation, f. In other words, represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, fm, i.e. f = fm.
Here is a simple FM signal:
Mathematical process of generating FM: (direct method)
Consider a CW signal with constant envelope but time-varying phase, so
Upon defining the total instantaneous angle
we can express xc(t) as
Conceptually, direct FM is straightforward and requires nothing more than a voltage controlled oscillator (VCO) whose oscillation frequency
Xavier University – Ateneo de Cagayan
Submitted by: Submitted to:
Dapal, Jamie Daisylette Engr. Mary Jean Apor
Fermano, Jerick James
Oraiz, Gerard James
Sabunod, Shane John
Siman, Lester C.
Objectives:
1. To obtain a frequency modulated signal via direct method
2. To understand the process of frequency modulation by direct method
Background Theory: Frequency modulation uses the information signal, Vm(t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:
Information: Vm(t)
Carrier: Vc(t) = Vco sin ( 2 fc t +
FM: VFM (t) = Vco sin (2 fc + (f/Vmo) Vm (t)t +
We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: f, the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: fc + (f/Vmo) Vm (t) now varies between the extremes of fc - f and fc + f. The interpretation of f becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency.
We can also define a modulation index for FM, analogous to AM:
= f/fm , where fm is the maximum modulating frequency used.
The simplest interpretation of the modulation index, is as a measure of the peak frequency deviation, f. In other words, represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, fm, i.e. f = fm.
Here is a simple FM signal:
Mathematical process of generating FM: (direct method)
Consider a CW signal with constant envelope but time-varying phase, so
Upon defining the total instantaneous angle
we can express xc(t) as
Conceptually, direct FM is straightforward and requires nothing more than a voltage controlled oscillator (VCO) whose oscillation frequency