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I am routing an 8-layer PCB, and need to have strict impedance control on one of my nets. The signal layer that the sensitive net is on is in between a ground plane and a power plane. Such as:

------- GND
------- Signal
------- Vcc

My question here is, will the capacitive nature of the two planes have an effect on the impedance of my sensitive net? Is it better to route high speed signals on internal layers or should I keep on outside layers under a solid ground plane?

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Yes, both planes will affect the impedance. Although it it nothing wrong with using a power plane as a reference plane.

When having impedance controlled lines between two planes, it is usually referred to as stripline. Can be symmetric (same distance to both reference planes) or asymmetric (not same distance to both planes).

Although, when using ground and power planes as references for a stripline, one should make sure the power plane is well decoupled to the ground plane (using decoupling capacitors).

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Yes, the added plane will affect the Zo of your trace.

But either way (routing on an outer layer or on an internal layer) will work. You need to adjust your trace width (make it narrower) on the inner layer to account for the additional plane, which is a return path for high frequency signals. There are many tools out there that can do the calculations for you. You want to model a stripline configuration.

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