Supplementary Information for "Real-Valued Gain Enabled Higher-Order Exceptional Point under Anti-Parity-Time Symmetry"

A. Real-valued variable gain enables a higher-order EP；B. Equivalence between the real-valued gain condition and a voltage source loaded with an equivalent real impedance；C. Derivation of the frequency shift response to the perturbation at the EP；D. Comparison of the sensitivity between the systems with different order EPs；E. Experimental setups and validations