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# [SOLVED]Why voltage or current ratios in dB have same Rs?

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#### CHL

##### Member level 3
Hello

When we calculate decibels,

dB = 10log(Po/Pi) = 10log{(Vo^2/R)/(Vi^2/R)} = 20log(Vo/Vi)

However, why the Rs are same?

In communication circuits, it is reasonable since the input and output impedances are 50ohm, same.

Even in other cases, we assume that the Rs are same.

What is the reason?

#### Audioguru

##### Advanced Member level 5
Decibels is the ratio of two powers or two voltages. Then the resistance is usually the same to make a simple comparison. Two 600 ohm microphones or two 8 ohm speakers.

#### CHL

##### Member level 3
Decibels is the ratio of two powers or two voltages. Then the resistance is usually the same to make a simple comparison. Two 600 ohm microphones or two 8 ohm speakers.

A simple comparison is possible, but it is not suitable for all cases.

For example, if we measure the input and output voltages of a simple common source amplifier, the input impedance and the output impedance are different.

Thus, the Rs are different.

I'm still confused.

#### godfreyl

##### Advanced Member level 5
IMO, it depends if you're talking about power gain (ratio of output power to input power) or voltage gain (ratio of output voltage to input voltage..

For power gain: dB = 10log(Po/Pi) = 10log{(Vo^2/Rload)/(Vi^2/Rin)} and the Rs can be different as you say.

For voltage gain: dB = 20log(Vo/Vi) and the Rs don't matter.

#### Audioguru

##### Advanced Member level 5
An extreme case of measuring the voltage gain in decibels is when the active device is an opamp with Fet inputs that have a resistance of more than billions of ohms and the output impedance of the opamp is much less than 0.1 ohms.

#### jiripolivka

##### Advanced Member level 5
IMO, it depends if you're talking about power gain (ratio of output power to input power) or voltage gain (ratio of output voltage to input voltage..

For power gain: dB = 10log(Po/Pi) = 10log{(Vo^2/Rload)/(Vi^2/Rin)} and the Rs can be different as you say.

For voltage gain: dB = 20log(Vo/Vi) and the Rs don't matter.

The Decibel is the RATIO OF POWERS. NOT voltages.
So if you have different impedances, you CANNOT relate voltages across them by decibel ratios.
But you CAN relate the powers.

Only in networks with the same in/out impedance like 50 o 600 Ohms, ONLY THEN you may relate voltages by decibel scale.

One proof is the use of "dBm" unit which expresses the POWER in milliwatts (hence "m"), or if you work in Watts, you may use "dBW".

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Sometimes people use "dBV" scales but it only holds for a specified impedance, mostly 50 Ohms.

#### FvM

##### Super Moderator
Staff member
Calculating power gain makes only sense if both in- and output are impedance matched. That's generally not the case in audio circuits. There impedance (e.g. 600 ohm microphone impedance) is only nominal, the gain can't be usefully expressed as power gain and actually never is by anyone working in this field. Same thing with most OP circuits.

Power gain is commonly used for RF circuits. Most of them has 50 ohm matching, in so far using the same reference impedance is at least the usual case. But it's not strictly required, my simple answer to your initial question is - we don't.

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P.S.: I agree to this Wikipedia definition
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity.
https://en.wikipedia.org/wiki/Decibel

dB is not restricted to power units. In accoustics we are e.g. applying it to sound pressure, that's not a power unit. Also a VU meter doesn't primarly measure a power, it's only nominally referring to the power delivered to a 600 ohm load, but is actually performing a voltage measurement.

#### godfreyl

##### Advanced Member level 5
The Decibel is the RATIO OF POWERS. NOT voltages.
So if you have different impedances, you CANNOT relate voltages across them by decibel ratios.
It may not be strictly correct, but it is common practice. For example, opamp datasheets normally express the voltage gain in dB.

#### CHL

##### Member level 3
A textbook, "Electronic circuits (Nilsson, Riedel)", explains it in Appendix D;

- When the input resistance equals the load resistance, we can convert the power ratio to either a voltage ratio or a current ratio.

However, as 'godfreyl' said, it is normally used in anywhere, such as opamp gain.

Should we just assume that the input and output resistances are always same when we calculate the dB?

#### FvM

##### Super Moderator
Staff member
Should we just assume that the input and output resistances are always same when we calculate the dB?
As said, dB calculation can be applied to different units. If the unit is voltage or current, you don't usually care for impedances. Except for the said case with equal impedances, where power dB numbers are also describing voltage ratios and vice versa.

CHL

Points: 2