This is the BBC character outline, as written by John Nathan-Turner and Eric Saward.
Perpugilliam (Peri for short) Brown is a wealthy 18-year-old American student studying botany. She had long blonde hair which complements her attractive looks. She does not suffer fools gladly, and her most charming attribute is an acute sense of humour.
We meet Peri for the first time while she is on holiday in whichever country we decide to film next season's foreign story.
Peri's mother Janine has remarried a man Peri dislikes--Howard. Peri still treasures the memory of her father, who died when Peri was 13, particularly as her mother seems to care more for Howard's three children than for Peri herself. It is because of her respect for her father that Peri thinks so highly of the Doctor--to some extent the Doctor replaces the gap in Peri's life. When he died he was of the same age as the Doctor appears now. This never develops further than admiration and close friendship.
Peri is the kind of girl who is popular not just because of her looks but because her warmth and sense of fun make her appeal to people of all ages.