Based on my very basic current understanding of decibels in electronics, it is said that I should use the
db = 10Log(p1/p2) formula if I want to calculate the power ratio in db between two values and the
db = 20Log(v1/v2) formula if I want to calculate the voltage (or current) db ration between two values.
Although I understand how these formulas are derived, I don't understand why we need two formulas (one for power and one for voltage), are two formulas really necessary? I am asking this because as far as I understand, the calculated db value by itself is just a ratio between two values and if that is the case, isn't a ratio just a ratio and nothing more?
In other words, in my head, a doubling of power or doubling of voltage is the exact same thing! Both values are being doubled so I would expect the same db ratio result from both comparison (power and voltage). Below are two examples:
Example for power:
P1 = 200; p2 = 100; db = 10Log(p1/p2) = 3 db.
Example for voltage:
v1 = 200; v2 = 100; db = 10Log(v1/v2) = 3 db ... (notice not using 20Log(v1/v2) formula here)
The logic above makes sense to me because I see doubling as doubling, it does not matter to me if we are doubling power or doubling voltage, both measurements are being doubled so why should't they have the same db value? Specially since we already specify watts or volts on the db units result (dBm, dBv dBu, dBc, etc)?
What am I missing?