Development of the PaK 40 began in 1939 with development contracts being placed with Krupp and Rheinmetall to develop a 7.5 cm anti-tank gun. Priority of the project was initially low, but Operation Barbarossa in 1941 and the appearance of heavily armoured Russian tanks like the KV-1, increased the priority. The first guns were delivered in November 1941. By 1943 PaK 40 formed the bulk of the German anti-tank artillery.
The PaK 40 was the standard German anti-tank gun until the end of the war, and was supplied by Germany to its allies. Some captured pieces were used by the Red Army. After the end of the war the PaK 40 remained in service in several European armies, including Albania, Bulgaria, Czechoslovakia, Finland, Hungary and Romania.
About 23,500 pieces were produced, and about 6,000 more were used to arm tank destroyers.
The PaK 40, essentially a scaled up version of the PaK 38 debuted in Russia where it was needed to combat the newest Soviet tanks there. It was designed to fire the same low-capacity APCBC, HE and HL projectiles which had been standardized for usage in the long barreled KwK 40 tank guns. In addition there was an APCR shot for the Pak 40, a munition which eventually became very scarce.
The main difference the among the rounds fired amongst by 75 mm German guns is in the length and shape of the cartridge cases for the PaK 40. The 7.5 cm KwK (tank) fixed cartridge case is twice the length of the 7.5 cm KwK 37 (short barrelled 75 mm), and the 7.5 cm PaK 40 cartridge is a third longer than the 7.5 cm KwK 40.
The longer cartridge case allowed a larger charge to be used and a higher velocity for the APCBC round to be achieved. The muzzle velocity was about 790 meters per second (as opposed to 750 m/s for the L/43 75 mm). This velocity was available for about one year after the weapon's introduction. Around the same time, the Panzer IVs 7.5 cm KwK 40 L/43 gun and the nearly identical Sturmkanone (StuK) 40 L/43 began to be upgraded with barrels that were 48 calibers long, or L/48, which remained the standard for them until the end of the war.
In the field, an alarming number of L/48 cartridge cases carrying the hotter charge failed to be ejected properly from the weapon's semi-automatic breech, even on the first shot (in vehicles). Rather than re-engineer the case, German Ordnance reduced the charge loading until the problem went away. The new charge brought the muzzle velocity down to 750 m/s, or about 10 m/s higher than the original L/43 version of the weapon. Considering the average variability in large round velocities from a given gun, this is virtually negligible in effect.
The first formal documentation of this decision appears on May 15 1943 ("7.5cm Sturmkanone 40 Beschreibung") which details a side by side comparison of the L/43 and the L/48 weapons. The synopsis provided indicates very little difference in the guns, which is horrible when you consider that guns are upgraded to be more effective, which appears not to have happened here.
All further official presentations of the KwK 40 L/48 ("Oberkommando des Heeres, Durchschlagsleistungen panzerbrechender Waffen") indicate a muzzle velocity of 750 m/s for the gun. As for the PaK 40, the desire for commonality again appears to have prevailed since the APCBC charge was reduced to 750 m/s even though case ejection failures apparently were never a problem in the PaK version of the gun.
For reasons which seem to be lost to history, at least some 75 mm APCBC cartridges appear to have received a charge which produced a muzzle velocity of about 770 m/s. The first documented firing by the U.S. of a PaK 40 recorded an average muzzle velocity of 776 m/s for its nine most instrumented firings. Probably because of these results, period intelligence publications ("Handbook on German Military Forces") gave ~770 m/s as the PaK 40 APCBC muzzle velocity, although post war pubs corrected this (Department of the Army Pamphlet No. 30-4-4, "Foreign Military Weapons and Equipment (U) Vol. 1 Artillery (U) dated August of 1955-this document was originally classified).
In addition, German sources are contradictory in that the Official Firing Table document for the 75 mm KwK 40, StuK 40, and the PaK 40 dated October, 1943 cites 770 m/s on one of the APCBC tables therein, showing some confusion. ("Schusstafel fur die 7.5cm Kampfwagenkanone 40").