This article designs and studies a low-injection sheet beam extended interaction oscillator (EIO) circuit that uses TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">51</sub> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> mode operation. Through the combination of theoretical analysis and particle-in-cell (PIC) simulation, the mode characteristics and output characteristics of the circuit are studied. Theory and dispersion analyses on the designed EIO demonstrated that the special circuit structure and the optimized cutoff frequency effectively suppress nonoperating lower order modes. Only TM <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">51</sub> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> mode can support effective beam–wave interaction in the designed EIO, which has a benefit of increasing the frequency and size of miniaturized devices. The designed EIO can achieve high-frequency microwave radiation output with higher energy under low injection (low current density and low voltage). At a certain surface loss, when an electron beam with 1 A and 19.6 kV is injected, the 0.36-terahertz (THz) radiation power of 200 W is achieved. The slow wave structure has been presented. The designed circuit structure can be applied to high-frequency THz radiation source devices.