All analog scopes have video delay lines for the signal to be displayed so the can trigger the sweep before it hits the phosphor
A cable is a distributed network of L, C with a characteristic impedance with a source load R to match to get a flat response with no echoes or high return loss.
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The Vbat ought to be a video source with same source impedance as Load.
It can be constructed with solid magnet wire around a form but should be at right angles or planar with ground plane.
Interwinding capacitance should be low by gapping each turn by >3d (wire) so they do not couple to each other.
Consider ground plane or tin/brass shield around it solder to ground plane with tabs.
Then choose your impedance eg. 50 or 100 Ohm and calculate L in nH then use a calc. for turns and diameter, D with wire thickness d.
Did you forget to match impedances ? L orientation or capacitive coupling?
More info
http://www.rhombus-ind.com/dlcat/app1_pas.pdf
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However your requirement must define bandpass ripple, phase shift and band reject levels to be testable .
Note that time or group delay in a bandpass is the derivative of phase shift over the band, so you can't have zero phase shift.
I really need a delay and not a phase shift