antenna gain, calculating voltage scaling
-4 dB in power is also -4 dB in voltage (since you are comparing voltages across the same impedance, 50 ohms).

In converting a voltage ratio we use 20log. In converting a power ratio we use 10log.  Thus the voltage will be reduced by a factor of 10^(-4/20) = 0.631.  Thus the 200 mV peak sinewave, reduced by -4 dB, will become 126 mV peak.