A circuit system of programmable BP on-chip learning neural network with learning rate adaptation is designed.The whole system comprises feedforward network and error back-propagation network.A novel programmable generator of sigmoidal function and its derivation is proposed.Its outputs include the sigmoidal function to realize I－V nonlinear transfer and its derivative using the forward differential method.Both functions fit well with the ideal functions.Moreover

the threshold and the gain factor can be easily programmable.Learning rate adaptation circuit is also presented to accelerate the convergent speed.Using a standard 1.2μm CMOS process

experiments such as sin(x) function fitness are done to the whole system.These experiments verify the superior performance of this on-chip learning BP neural network.