Assume valve cut-off as grid is biassed well negative.
Capacitor Ct will charge accordingly.
When grid made much more positive (i.e. +ve pulse)
Valve conducts, capacitor discharges (linearily).
Anode voltage falls; this fall is fed back thru capacitor Ct which will tend to oppose the original change of grid polarity.
This effect means that the grid voltage in fact varies almost nil!
However; the anode voltage falls in a linear fashion until anode bottom is reached THEREFORE; the voltage decrease is linear because the discharge current through the capacitor is constant!
Circuit derives its name from Miller effect (in vacuum tubes) which multiply's grid-plate capacitance by ( +1) the actual (small) grid-plate capacitance; (this is nullified by a screen grid).
The operation of the circuit can also be controlled by variation of the suppressor grid voltage.
Edwin Armstrong discovered in 1915 that oscillation occurs in triode amplifiers by this inter-electrode capacitance when the anode load was inductive (and below resonance)
In 1919 John Miller of the US bureau of standards
presented a mathematical analysis of the phenomina and the effect that now bears his name!

Suggested schematic is a development of above.
Cathode follower isolates the anode from capacitance connection i.e. Hi to Low impedance convertor.
From: A simple all-valve 1-inch oscilloscope by Ian Wilson K3IMW


Dr F.C.Williams was a young wartime radar boffin.
He was well known for his birdsnest breadboard circuits which often left the board,
trailed across the bench, and over the edge.
He was also known to comment on circuits with "Oh! Very sanitary!" or "Phantastic!"
In those days, time bases and the delay of pulses tended to depend on an exponential rundown due to the simple RC arrangements used.
He worked on linearising the rundown to improve stability, by using "Miller" feedback.
His pulse-stretching circuit using 2 pentodes + 2 diodes was named the very sanitary Sanatron
and the single pentode version became the phantastic Phantastron.

In more sophisticated (WW II) radar equipment a much more linear timebase was needed and also for precise and adjustable time delays.
To acheve this BLUMLEIN developed what is commmonly known as the "Miller Integrator".
His patent 560,527 explains its principles and goes on to give a sample of each of two applications.
These initiated a whole series of circuits using diodes as auxiliaries and included the celebrated "phanstastron" and "sanatron"
During the war such patents were not published and it seems the basic circuit was covered by A C Cossor Ltd and J W Whiteley a few months earlier.
Actually Blumlein's invention was the earlier, but owing to the elaborate secrecy procedure some time elapsed before the application could be filed.

Hand-built minature oscilloscope using Miller linear sawtooth sweep oscillator (as detailed above)