Say I am in a military aircraft with a non-AESA radar. The radar is set to scan 4 elevation bars, so when I fly level, 2 above and 2 below the horizon.
If I pitch 20 degs up, will it continue to scan around the horizon or will the bars move up with the aircraft pitch?
If i understand your question, you are asking whether the vertical elevation direction of the radar antenna lobe is corrected for when the aircraft is in a pitched up position as compared to a level position. (Whether this correction would be done mechanically in older radars or electronically with AESA radars is secondary)
It probably depends on the particular aircraft and version. But to my knowledge it is generally not. The antenna will keep its direction within the host aircraft and thus scan a higher altitude volume when the aircraft is pitched up.
Note that the pilot can change the vertical elevation range of the antenna by tilting it up or down manually at any time (if it is not locked on a target) and will probably do so in order to compensate for longer phases of pitch up flight.
As an example, this document is a description of the AN/APG-66 and -68 radar systems of the F-16 Fighting Falcon. (It is a documentation for a general public simulator game, but you can be confident that it describes the function of the real aircraft very accurately) See page 11, section "Elevation". In the case of the F-16, the antenna tilt interface is part of the HOTAS controls, on the throttle: http://falcon4.wikidot.com/avionics:hotas, see "Antenna Elevation Knob"
When a target is "tracked" or "locked" this is another matter. In that case, the antenna will generally move autonomously in order to keep the target within the center of its detection lobe as long as possible, both vertically and horizontally (azimuth), within what is physically possible taking into account the attitude of the host aircraft versus the target. (See the doc for this also)
Without knowing what radar system you are dealing with, I will answer generally.
An AESA relies on an array of normally dipole antennas which are phase adjusted to enhance the gain in a certain direction. In a non-AESA environment, an antenna such as a forward looking radar antenna is normally a dish. The dishes are mechanically articulated to change the focus gain of the antenna to a different spot. Some articulate vertically only, but there are some which can articulate laterally. Additionally, some can alter polarization.
If your radar is a WX radar unit, then normally just the pitch, or elevation is adjustable. Some targeting radars allow lateral articulation which helps scan, identify and track targets both vertically and laterally.
To answer the OP question, if the aircraft is pitched up 20 degrees, and the radar is coupled to the aircraft pitch, then you can expect that the dish would pitch downward. Although, in this example, 20 or 30 degrees is about the limit of most of the radar units I have worked with.
Finally, modern AESA antennas can create multiple beams, which permit active and concentrated energy on selected targets. A non-AESA dish antenna does not really have that capability, although several strategies and methods were used, particularly before the development of aircraft PESA and AESA antennas. A PESA by definition has one lobal pattern, which can be articulated. An AESA may have more than one.
