There is so much information on the internet about the efficiency of EFHW antennas and to be honest I'm not going to write a long article into the technical measurements of dB loss through two transformers setup using a VNA.
However, what I thought I would do is take some of the Interweb efficiency numbers for 49:1 EFHW transformers based on Fair Rite mix 43 efficiency and plug some numbers representing the Watt's out from the transceiver into a 49:1 transformer and Watt's out from your antenna.
It seems that the general accepted dB loss for a mix 43 core is somewhere between -.72dB and -1.2dB depending on who has tested the transformer. Some people and manufacturers quote -.02dB loss but I'm going to ignore that for now because I for one not believe leprechauns exist . These variance in numbers seems to be due to the size of a core and the way the transformer is wound.
I have also take a number for an EFHW suggested ground loss of 1.4% (AA5TB site).
So lets do some simple maths assuming your transceiver is putting out 10 watts with a 3 meters of RG174/U then 4.5m of RG58 (both of these coax's are commonly used for portable operations) RG58 if often used for longer runs. Then into an EFHW transformer and onto the antenna with feed point resistance of 2450 Ohms with an SWR of 1.5:1.
We are assuming 14mhz transmission.
So here we go.
For 3m of RG174 you will have a coax loss of approx. .3db your 10w is now 9.33w
For 4.5m of RG58 you will have a coax loss of approx. .2db your 10w is now 9.55w
We then put the remaining power through an efficient EFHW transformer and a less efficient transformer.
Your 9.33w (RG174) into a -1.2dB transformer reduces your watts to 7.07 watts output to the antenna
Your 9.33w (RG174) into a -.72dB transformer reduces your watts to 7.90 watts output to the antenna
Your 9.55w (RG58) into a -1.2dB transformer reduces your watts to 7.24 watts output to the antenna
Your 9.55w (RG58) into a -.72dB transformer reduces your watts to 8.09 watts output to the antenna
Finally you need to remove ground losses.
Your 9.33w (RG174) into a -1.2dB 7.07 watts output less 1.4% give you 6.97 watts output
Your 9.33w (RG174) into a -.72dB 7.90 watts output less 1.4% gives you 7.79 watts output
Your 9.55w (RG58) into a -1.2dB 7.24 watts output less 1.4% gives you 7.14 watts output
Your 9.55w (RG58) into a -.72dB 8.09 watts output less 1.4% gives you 7.98 watts output
If you multiply the worse case scenario above into a transceiver putting out 100w you will radiate 72.4 watts or a 25% loss in power. OMG!!!!! were never going to get any contacts!!!
Well that's not true there are a lot of antennas out there which are less efficient than the humble EFHW and remember 100w in and 72.4 watts out is about 1.4db loss or 1/4 of an S point on a meter!
A couple of other points.
The loss in the transformer is turned into heat! This is why we have different transformer sizes for different powers. Duty cycle also plays a part in the heat dissipated through a transformer. You will always be able to have more SSB watts into a transformer than CW or Data.
It is also possible to optimise the windings on a transformer to suit different ranges of bands and stack more cores to get better efficiency. However a 49:1 transformer is a good compromise.
Some comments on Coax and SWR
If you have higher SWR at the antenna your coax loss will be higher.
The higher in frequency than 14mhz you go the more losses in the coax.
Losses below 14mhz will be less. For example at 7.1mhz about 30% less.
So I hope this blog helps you understand the relationship between each part of the antenna and where you lose your radiated power.