We're going to use area ratios and lever ratios to do this transformer thing.
Area ratios: The tympanic membrane's vibrating area is about 55 square mm. The footplate of the stapes' vibrating area is about 3.2 square mm. If we apply a force on the tympanic membrane, that force is going to be amplified as we measure the force per area at the footplate of the stapes.
Ex: Arrow on cone. Force pressing down is f1. Force at bottom of cone, f2, has a tremondous increase in force, so it is greater than the first. So if we take the TM's 55 and divide by stapes' 3.2, we get a 17, or a 17:1 ratio of the area. So it's a 17:1 area ratio.
Lever ratios: Look at the teeter-totter like diagrams. The fulcrum (balance point) is different on each one. In the left one, if you press down on d2, the lift is the same ford1---sod1=d2. Inthe one on the right, if you press down on d2, then you're lift in d1 is going to be less than d2. So if you're in a situation like the one on the right, and you want to lift a rock or heavy object, you want to place your instrumenation so the rock is on d2, and you're on d1. So you will get an enhancement of force on d2 to lift the rock.
Example: malleus is rotating around that black dot, the fulcrum. The distance from that pivot point/ fulcrum down to the end of the long process of the malleus is measured, and then the same thing is done for the incus distance. The malleus distance is larger than that of the incus, in a 1.3:1 ratio. The malleus has a 1.3:1 lever ratio.
So now we take the 17 from the area ratio and the 1.3 from the lever ratio and we multiply them to get a 22:1 ratio. A 22:1 sound pressure ratio corresponds to 27 db. So this is how the middle ear acts as an impedence transformer/transducer from the ear canal to the fluids of the inner ear.