In the future power-electronics-dominated power systems

grid-forming (GFM) converters have been regarded as important devices to actively establish frequency and voltage

so as to provide essential grid support. However

due to their voltage source behavior and emulated swing dynamics

GFM converters may encounter low-frequency oscillations (LFOs) when connected to strong grids

which belongs to the self-stability problem of GFM converters. Moreover

GFM converters will also interact with grid-following (GFL) converters and thus impact the mid-frequency oscillations (MFOs) induced by phase-locked loops (PLLs). It has been preliminarily shown in the literature that GFM converters can help stabilize the PLL-induced MFOs

but currently

there is a lack of systematic design methods to coordinate the self-stability and stabilizing ability of GFM converters. This paper addresses this gap by revisiting the impedance model of a typical GFM converter and briefly analyze the oscillations caused by converters. Based on our analysis

we propose a frequency-partitioned synthesis design framework to enable dynamic virtual impedance (DVI) in GFM converters

aiming to enhance their self-stability and stabilizing ability simultaneously. Particularly

a self-stabilizing module is designed to ensure robust device-level damping

with control parameters auto-tuned using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{H}_{\infty}$ methods. In parallel

a stabilizing module is introduced to stabilize GFL converters and enhance the system-level stability

which utilizes a perceive-and-optimize tuning strategy. Simulation results validate the effectiveness of the proposed synthesis DVI framework.