A VCO (Voltage-Controlled Oscillator) does not inherently produce only FM signals. However, it can be used as a direct FM generator when the message signal is applied to its control input.
How a VCO Produces FM
A VCO has a control-voltage-to-frequency relationship given by:
\[ f_i(t) = f_c + k_f v(t) \]
where:
- fc = carrier or center frequency
- v(t) = input/control voltage
- kf = frequency sensitivity of the VCO (Hz/V)
- fi(t) = instantaneous frequency
Suppose the message signal is:
\[ m(t) = A_m \cos(2\pi f_m t) \]
If the message signal is applied directly to the VCO control input, then:
\[ v(t) = m(t) \]
Therefore, the instantaneous frequency becomes:
\[ f_i(t) = f_c + k_f A_m \cos(2\pi f_m t) \]
This means that the instantaneous frequency continuously moves above and below the center frequency fc according to the amplitude of the message signal. This is the basic principle of frequency modulation (FM).
Peak Frequency Deviation
The peak frequency deviation is:
\[ \boxed{\Delta f = k_f A_m} \]
The FM modulation index is:
\[ \boxed{ \beta = \frac{\Delta f}{f_m} = \frac{k_f A_m}{f_m} } \]
Example
Consider a VCO with:
- Carrier frequency: fc = 100 kHz
- Frequency sensitivity: kf = 5 kHz/V
- Message amplitude: Am = 1 V
- Message frequency: fm = 1 kHz
The instantaneous frequency is:
\[ f_i(t) = 100 + 5\cos(2\pi \times 1\,\text{kHz}\,t) \quad\text{kHz} \]
Therefore, the output frequency varies between:
\[ f_{\min} = 100 - 5 = 95\,\text{kHz} \]
and
\[ f_{\max} = 100 + 5 = 105\,\text{kHz} \]
Thus, the frequency continuously varies between 95 kHz and 105 kHz in accordance with the message signal. This is an FM signal.
Summary
A VCO can be used as a direct FM generator. When the message signal is applied to the VCO's control input, its instantaneous output frequency varies proportionally with the message amplitude, thereby producing an FM signal.