The word circuit does not occur in Domesday Book.
It is a modern coinage, used to emphasise a significant feature of the Domesday Inquest, namely that it was conducted by royal commissioners, each responsible for one group of counties. Each circuit has its own characteristic features, and an appreciation of these is necessary in order to understand what material is included and how it is recorded. Where a circuit consistently provides information entirely lacking in a neighbouring circuit, it is unlikely that this indicates a real difference between the two. If we were to take Domesday Book literally, for instance, Cambridgeshire was bursting with Anglo-Saxon overlords before the Conquest while not one was to be found in the adjacent county of Lincolnshire. The circuit boundary between the two, and the whims of the two panels of commissioners, is the more plausible explanation.
Since the word circuit does not appear in contemporary sources, the circuits themselves must be reconstructed from indirect evidence. The survival of two manuscripts which have been identified as circuit returns for East Anglia (Little Domesday Book) and the south-western counties - Liber Exoniensis - provides a secure starting point.
For other counties, the content, formulae, vocabulary, and internal structure of their entries are the clues to the circuit to which they belong. In most cases, these are sufficiently distinctive for historians to be in broad agreement on the composition of the remaining circuits. In essence, there were six circuits in Great Domesday, each forming a territorial block, each block composed of 5 counties (if Rutland is counted as a separate county, there were 6 counties in circuit 6). Little Domesday contained the 3 remaining counties of Essex, Norfolk, and Suffolk.
The circuits of Great Domesday were:
Circuit 1: Berkshire, Hampshire, Kent, Surrey, Sussex
Circuit 2: Cornwall, Devon, Dorset, Somerset, Wiltshire
Circuit 3: Bedford, Buckingham, Cambridge Hertford, Middlesex
Circuit 4: Leicester, Northampton, Oxford, Stafford, Warwick
Circuit 5: Cheshire, Gloucester, Hereford, Shropshire, Worcester
Circuit 6: Derby, Huntingdon, Lincoln, Nottingham, Rutland, Yorkshire
For the methodology employed in reconstructing the circuits, see Carl Stephenson, 'Notes on the composition and interpretation of Domesday Book', Speculum, vol. 22 (1947), pages 1-15.