Recently, the dual-permanent-magnet-excited (DPME) machine has attracted growing attention due to its high torque density. Due to the bidirectional field modulated effect (BFME), airgap flux density harmonics (AFDHs) are more complex and abundant than traditional permanent magnet synchronous machines (PMSMs). Moreover, the back-electromotive force (EMF) generated by AFDHs is also complex. Unfortunately, only a few papers qualitatively analyze back-EMF. The qualitative analysis for back-EMF can reveal some important conclusions; for example, only AFDHs meeting specific pole pair numbers (PPNs) can generate back-EMF. However, it may also ignore some details and valuable findings. In this paper, a purely analytical magnetomotive force (MMF) permeance model (PAMPM) for a DPME machine is built to quantitatively analyze the back-EMF. The PAMPM does not require a numerical method, such as conformal transformation. With the PAMPM, AFDHs that contribute to the generation of back-EMF can be recognized and quantified. Interestingly, AFDHs with m_2p_2=np_3 cause PM flux-linkage to have a dc bias, and not all AFDHs play a positive role in the generation of back-EMF. The main recognition results are as follows: 1) the S-II and R-II types of AFDHs in a 12/10 DPME machine overall make a negative contribution to the generation of back-EMF; and 2) AFDHs with PPN=22 in the two types mainly cause a negative contribution. To further verify the above results, 2D finite element simulation and experimental tests of a prototype machine are also conducted.