I have designing microstrip patch antenna and was getting gain and directivity as around 9.5 dB and 8.7 dB approx.But I was getting the value of efficiency in negative.
The antenna efficiency (or radiation efficiency) can be written as the ratio of the radiated power to the input power of the antenna: Er = (P radiated / P input)
As told earlier , gain = efficiency* directivity, you can easily get the efficiency or if you use any software like HFSS or ADS there is a provision that directly plot the efficiency curve and you verify your result..
@Andrew - just a comment. We can't divide two numbers expressed in dB scale (log scale) to find the efficiency. First they need to be converted to absolute scale and then divided. The efficiency 1.09195402299 you suggested was by dividing G and D in dB scale. We can't do that before converting each of them to their absolute values
Alternately,
G = Er * D
or, 10log (G) = 10 log (Er) + 10 log (D)
therefore Er in dB = G in dB - D in dB as rightly pointed out by Russell
If gain is larger than directivity it means the efficiency is larger than one. I guess your simulation may not have achieved convergence, there should be some trouble in your simulation.
Negative efficiency means power amplification, unless your antenna is not active it is not physical.
According to gain and directivity values of your images, the efficiency of 52.96 is correct. Even you have not shown efficiency plot.... do you have it, can u show me?
yes, gain = efficiency*directivity, but efficiency is always between 0 and 1, so of course it is a negative number in dB scale. An efficiency greater than 1 (i.e. more than 100%) or, in other words, greater than 0 in dB scale, has no physical sense for an antenna as it is, because it is a passive component.
Be careful: "total efficiency" takes into account also the impedance mismatch at your simulation port, which is different from the radiation efficiency of your antenna.