The Fairfax County Board of Supervisors yesterday approved controversial amendments to the county's cable television ordinance that supporters say will make it among the strictest in the nation.

The amendments, which call for extensive financial disclosure by all companies seeking the county's lucrative cable TV franchise under threat of a felony penalty, are aimed at discouraging lobbying techniques that have plagued cable franchising in many of the nation's largest cities.

"This [ordinance] really is tough," said Fairfax board chairman John F. Herrity, a Republican. "I hope this clears up some of the potential criticism and gives us cleaner air to work under. We've tried so hard to do this right."

County officials said the amendments will not delay the process of getting cable television service to the county's 200,000 households. The beginning of cable construction is now expected by the middle of 1982.

Under the amendments approved yesterday, each commercial cable applicant will be required to make public the names of its stockholders, as well as the names of any officer or employe known to hold an interest in the company. Companies also must disclose gifts or campaign contributions to county officers, employes and their families.

The amendments further require that county supervisors and all county employes who deal with cable television disclose under oath their cable holdings and those of their families.

Virginia law provides that misrepresentation under such an oath constitutes perjury, and is punishable by up to 10 years' imprisonment and a fine of $10,000.

The board also gave preliminary approval to a measure requiring cable applicants to disclose expenses incurred in seeking the county's cable franchise. The measure is aimed at so-called "rent-a-citizen," a practice in which cable firms bestow company stock on prominent local citizens in return for lobbying services. Such awards have ranged as high as half a million dollars per company in some major cities, according to government and industry experts. p

A proposal to study the economic impact of "rent-a-citizens" on local cable rates is expected to be approved in Fairfax within the next few weeks. Industry experts say the practice can boost cable subscription rates paid by consumers by as much as 25 percent.

The board also gave preliminary approval yesterday to a measure that would require that applicants periodically disclose the names of all company lobbyists.

In other action, the supervisors approved a 12 percent increase in bus and Metro rail fares for county residents. The board, which has often blamed rapidly rising costs on poor Metro management, earlier rejected proposed increases of up to 31 percent sought by the Washington Metropolitan Area Transit Authority.

County transportation director Shiva K. Pant argued the fare increases, which are expected to raise about $600,000 during the remaining half of the fiscal year, are necessary to offset the county's share of Metro's deficit.

Fairfax's Metro bill is expected to top $21.1 million for fiscal year 1981, a 25.6 percent increase over last year. Metro officials have attributed the increase to the rising cost of labor, fuel and spare parts.

Even with the increase, county commuters will pay only 35.5 percent of the cost of their rides through the fare box, Pant said. The remainder is covered through the county's real estate taxes.