Frequency modulator sensitivity and Quadrature demod gain

```In the GRC Frequency mod block  the doc says
```
```
analog_frequency_modulator_fc
make(float sensitivity) -> frequency_modulator_fc_sptr
Frequency modulator block.
float input; complex baseband output
```
Takes a real, baseband signal (x_m[n]) and output a frequency modulated signal (y[n]) according to:
```
```
Where x[n] is the input sample at time n and  is the frequency deviation. Common values for  are 5 kHz for narrowband FM channels such as for voice systems and 75 KHz for wideband FM, like audio broadcast FM stations.         In this block, the input argument is , not the frequency deviation. The sensitivity specifies how much the phase changes based on the new input sample. Given a maximum deviation, , and sample rate , the sensitivity is defined as:
```        Constructor Specific Documentation:
Build a frequency modulator block.
Args:
sensitivity : radians/sample = amplitude * sensitivity

```
There is somejhing missing at:   " Where x[n] is the input sample at time n and  ____________  is the frequency deviation"
```

```
Here https://wiki.gnuradio.org/index.php/Frequency_Mod the same is missing too.
```
```
I guess it refers to  sensitivity = K = (2*pi*freq_deviation)/samp_rate    correct?
```

Second question related to this one.

```
If I the use Quadrature_demod for demodulation of the signal, the gain parameter will be the inverso of this one isnt it?
```

```
gain=samp_rate/((2*pi*freq_deviation)   but when I insert the quadrature demod block it is autofilled with
```
samp_rate/(2*math.pi*fsk_deviation_hz/8.0)   where does the 8.0 come from?

best regards

```
• Frequency modulator sensitivity and Quadrature demod gain Fernando