Confusion with transient analysis and initial condidtions in LTSPice

For a transient analysis (.tran), initial conditions are derived from a calculation of the DC operating point of the circuit (an implicit .op), assuming all voltage and current sources have fixed values. Source values are obvious for fixed-value sources, but for sources that change over time, such as PULSE() and SIN() functions, they are evaluated at time \$t=0\$, and any change thereafter is completely ignored.

All capacitors are ignored, since under unchanging conditions, capacitor current will always fall to 0A and remain there, and capacitor voltage will eventually settle at whatever DC potentials exist without the capacitor there at all. Inductors are replaced by a short-circuit, since their voltage will have settled at 0V, and at DC the current through them will eventually be whatever current would flow through a short-circuit there instead.

Initial conditions (DC operating point) are therefore calculated as if there are no time-varying elements present at all, time \$t\$ doesn't appear in any of the calculations. They represent conditions that would be present if the circuit had been powered on, and left for all eternity to settle into a steady state, during which no voltage or current sources deviated by even the tiniest amount. These are the conditions used to determine initial capacitor voltages, and initial inductor currents.

Then the transient analysis begins, and because things are now changing over time, capacitor and inductor voltages and currents are changing. Whatever their average values become over time will obviously be different from those calculated under the naive assumption that nothing ever changes.

When you say "initial charging of C4", be careful. C4 was assumed to be charged to some some fixed voltage during the DC operating point calculations of static state, before time existed, but its average charge over time (and in the future) can be very different, once the circuit starts to experience dynamic conditions, since it is only when time is considered that the truth can be known.

You can tell the simulator to skip the DC operating point calculations, and assume that all capacitors have 0V across them, and all inductors have 0A through them at time \$t=0\$, prior to beginning the transient simulation, using the uic flag in the .tran directive:

.tran 100m uic

You can tell the simulator what initial DC voltage to assume for a named node, ignoring whatever value it calculated during .op, using .ic:

.ic V(some_node)=5

In the following circuit, .op would correctly surmise that after a long time, capacitor voltage will have risen to, and settled at, \$V_X=+5V\$:

The simple .tran will demonstrate \$V_X\$ starting at +5V and staying there for the rest of time, since the capacitor is already charged to 5V:

Adding a uic to the .tran will have the capacitor begin with no charge, corresponding to \$V_X(t=0)=0{\rm V}\$. With no charge at time \$t=0\$, obviously the capacitor's voltage will increase from zero over time, in the expected exponential manner:

Using .ic we can say explicitly what state the capacitor shall have, prior to beginning the transient analysis. The .icV(x)=3 will cause capacitor voltage to begin at 3V, and rise from there:

Now changing the voltage source to an AC oscillation about a DC average of +5V:

The starting value at \$t=0\$ of the SIN() directive evaluates to +5V, no surprise, since \$5+sin(0)=5\$. and this is the value that .op uses to calculate starting conditions. You see above that \$V_X\$ does indeed start at +5V, but this is at a point in the cycle where V1 is rising, so .op predicted conditions at time \$t=0\$ which are not correct for a system that has been running for years. However, you do see that over time the capacitor does eventually adopt the expected average charge, where \$V_X\$ oscillates around +5V.

The next logical question is what would be the value of \$V_X\$, at each instant when V1 passes upwards through its +5V mean, assuming that the system had already been running for a while? In other words, what is a more appropriate \$V_X\$ at \$t=0\$? You could use algebra to figure it out, or you could do as I did, let the simulator predict that for you - I measured \$V_X\$ at \$t >> 0\$, as V1 passed upwards through +5V, and found it to be +4.96V. Set initial \$V_X\$ to exactly that:

Here we see that by setting initial conditions to predicted correct values, rather than allowing .op to "guess" them, produces the correct, expected, long-term behaviour, right from the start, from \$t=0\$.