# Arithmetic between response and impedance

#### keantoken

##### Registered
REW doesn't want to do arithmetic between frequency and impedance data, but there is actually a good reason for doing this. Multiplying a driver's frequency response with it's impedance gives you the driver's diaphragm acoustic response (or alternatively it's response if using current drive). I was hoping to do this with a range of drivers to see how cone shape affects response.

#### John Mulcahy

##### REW Author
What would the units of the result be?

#### keantoken

##### Registered
How does REW determine dbW without input of the speaker nominal impedance? Probably some similar logic would be used here.

In a speaker motor, force in newtons = BL*I where I is the speaker current. So current drive results in a even force response of the voicecoil. So the unit would be something like SPL per unit force or unit current. But REW doesn't take TS parameter inputs, hence the question above.

I suppose the sensible thing would be to make it SPL per unit current since the speaker impedance is the coil voltage at 1A current drive. So the unit would be SPL per amp RMS. This way we don't need TS parameter inputs for the unit to be sensible.

EDIT: Maybe the unit should be SPL/BLi which you can look at and know how to calculate what you need.

#### John Mulcahy

##### REW Author
dBW uses the reference impedance entered in the RTA Appearance settings.

I wouldn't want to add a further Y axis option for what seems a fairly esoteric requirement. Sticking with an SPL axis, what SPL value should result from (for example) a point on the graph where the frequency response is 75 dB SPL and the impedance is 8 ohms, assuming they have the same phase? 93 dB SPL? 84 dB SPL? Something else?

#### keantoken

##### Registered
I won't ask for a new unit for the Y axis, I just want to be allowed to do the operation. What about a check box or button in the error message to allow it?

#### John Mulcahy

##### REW Author
I can allow it, but I need to know what the answer should be, hence my question.

#### keantoken

##### Registered
Sticking with an SPL axis, what SPL value should result from (for example) a point on the graph where the frequency response is 75 dB SPL and the impedance is 8 ohms, assuming they have the same phase? 93 dB SPL? 84 dB SPL? Something else?
If we assume a measurement of 2.83Vrms at 1W at 1meter, then we can determine the voicecoil current based on the speaker impedance. Then we divide the SPL by that current. So

Force response = SPL / (2.83Vrms/Z)

This would give the force response for the conditions of the original measurement, assuming the voltage is correct.

#### keantoken

##### Registered
Well, for the trace arithmetic I just wanted to multiply the impedance by the sound pressure, so it would be something like

log20( Z * 1.122^SPL )

But that loses the original measurement units. The previous post should be converting SPL to non-logarithmic units.

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#### John Mulcahy

##### REW Author
I have allowed SPL * impedance or SPL / impedance in trace arithmetic operations for the next build. It seemed like some form of normalisation should be applied, so I normalise the impedance to the ref resistance for power figures which is configured in the RTA appearance settings. A little awkward, but that way where the impedance matches the reference value the resulting SPL will be unchanged, which seemed appropriate.