A complete harmonic phrase unit (i.e. T-PD-D-T) can be said to be a tonic expansion, that is, the whole unit is taken as an elaboration of the tonic. (You will appreciate more of this as we proceed further along in this course.)
However, a harmonic phrase need not be in its complete form, that is, certain functional element(s) may be omitted. For example, a phrase may begin with a PD chord or even a D chord. If it ends with a D-T, a perfect cadence is created, but if the closing T is omitted, we have an imperfect cadence.
Here are some examples from Harmony in Context:
Ex. 2.1 - T-D for first phrase, followed by D-T for answering phrase (note: no PD in both cases)
(A similar instance--a beautiful one from Mozart--is Ex. D.1b)
Ex. 2.7 - both phrases start with an implied D
Relation with melodic phrase
A particular melodic phrase may consist of one or more harmonic phrase units which can be in turn hierarchically related.
Ex. E.7a - The 4-bar melodic phrase is supported by the progression I - V6/5 - I - IV - V(6/4 - 5/3) - I; on this level, the functional progression is T-D-T-PD-D-T. In other words, it is as if the opening T-D-T overlaps with T-PD-D-T. We may construe this hierarchically, taking the opening T-D-T as a tonic expansion; of course, at the melodic phrase level, the whole progression is a tonic expansion:
I - V6/5 - I - IV - V(6/4 - 5/3) - I
T - D - T - PD - D - T
T ------------- PD - D - T
T ----------------------------------------
We will elucidate this hierarchic dimension of tonal harmony further under "Harmonic Expansion".
Terminological Clarification
! Note that Laitz uses the term "Phrase model" to refer to the T-PD-D-T harmonic motion (2008: 291). I use "Harmonic phrase model" to distinguish it from melodic phrase structures/models.