Passing through a sharp turn with an edge-coupled differential pair, the outside trace travels further than the inside trace. The difference in distance traveled contributes a small amount of skew to your differential signals. The skew acts as a mode converter, changing part of your differential signal power into common-mode power.
The pair-turning skew becomes noticeable only when the skew that the turn contributes rises to a level comparable with the natural skew already coming out of your driver. Therefore, before worrying about turns, first determine the skew of your driver. In many cases, the driver skew is not specified, in which case you can assume the skew will be at least 10% or maybe more of the signal rise time. Digital differential drivers just aren't balanced very well. Analog transceivers often are, which accounts for the importance of meticulous skew matching in some analog applications.
For example, let's say an Ethernet 100BASE-TX LAN transceiver with a well-balanced output transformer and common-mode choke puts out differential signals balanced to one part in 1000-meaning that the common-mode output is 1000 times smaller than the differential signal. To avoid amplifying the common-mode signal on the wires (and thereby the radiation), all components used with this transceiver must contribute skew on the order of one one-thousandth of one rise time or less. The rise time of a 100BASE-TX signal is approximately 8 nsec, corresponding to roughly 94 in. of propagation in air, one one-thousandth of which works out to 0.094 in., so the skew budget within cable connectors and board layout should be set somewhere around 0.1 in. Worrying about a minute skew effect much smaller than 0.1 in. doesn't help.
To take a faster example, a 2.5 Gbps serial-link driver with a rise time of 200 psec has an output skew of probably no better than 20 psec (maybe a lot worse). In this case, a skew budget of perhaps 20 psec seems reasonable.
Figure 1 illustrates the skew calculations for three alternative corner treatments, each with a trace pitch (centerline to centerline) of p. In each case, the two traces within the pair share the same number and type of sharp corners (shaded darker blue). The differences between the inside and outside traces are pink. The total lengths added to the outside traces are 2p, 1.65p, and 1.57p, respectively, for the three corner styles. Apparently, chamfering or rounding of differential corners does not eliminate skew; it only makes at best a modest improvement.
If your trace separation p equals twenty mils, and the propagation delay of your media is 160 psec/in., the total skew accumulated when rounding a corner of any of the three types in Figure 1 would range from a high of 2×(0.020 in.×160 psec/in.)=6.4 psec to a low of 1.57×(0.020 in.×160 psec/in.)=5 psec. If this amount of skew is superseded by the skew from your driver, then don't worry about the turns.
When skew becomes a problem, you can mitigate its impact in two ways. First, use a smaller spacing. The smaller you make p, the less skew you will get. This is one of the few benefits of tightly coupled pairs. Second, position your ICs so the traces leave the driver headed in the same direction in which they enter the receiver. For example, a differential pair that starts out headed north and ends up headed north has by definition equal numbers of right- and left-hand turns no matter what happens in the middle (unless it makes a spiral), so the net skew accumulated is zero.