Many of the trials have been held in closed sessions, sometimes without defence lawyers or family members being present.
Police seized Zarganar's computer and several banned films, including the latest Rambo movie, featuring the US-Vietnam war veteran taking on the former Burma's ruling military on behalf of Christian ethnic Karen rebels.
His sister-in-law, Ma Nyein, told the Reuters news agency: "He got 45 years for only three charges. More sentences will be passed on four remaining charges on Monday."
Family sources said police also found a copy of the leaked video of the lavish "champagne and diamonds" wedding of Senior General Than Shwe's daughter, which caused outrage among ordinary people in what is one of Asia's poorest countries.
The same court inside Yangon's Insein prison also sentenced two other dissidents, including a prominent journalist, to 15 years in prison and another man to 29 years, Ma Nyein said.
Rights groups say the jail terms are intended to eliminate all political opposition before an election in 2010, the final stages of a "roadmap to democracy" meant to bring an end to nearly half a century of military rule.
Western governments have dismissed the roadmap as a sham.
Other dissidents sentenced this week include a hip hop star who got six years for being part of a youth political group called Generation Wave, an opposition spokesman said on Friday.
In all, well over 100 people from across the spectrum of the democracy underground, including 20 women and Buddhist monks, have been condemned to up to 65 years.
The most prominent activists have been sent to the furthest corners of the country, making it almost impossible for relatives to deliver food and medicine to them, raising the possibility of the prisoners dying behind bars.
The US and European countries have condemned the ruling military's closed-door trials and sentences, although there has been little comment from countries in the surrounding region.