Somewhere in the stack of papers piled high on Professor David Rhodes' desk, there's a black A4 book full of scribblings.

"This is what I do in my spare time," he says excitedly, pointing at page after page of outrageously complex equations. "Some people can't understand it, but it's what I love doing."

Professor Rhodes, engineering genius and chairman of a market-leading Plc, is a startlingly intelligent man. The Doncaster-born Leeds University graduate has more letters after his name than most people have in all their names put together.

Over the past 25 years, he has built Filtronic from a two-man operation in the garage of his Leeds home into the most successful business ever to grow out of a United Kingdom University.

Today Filtronic is based at Saltaire and employs around 3,000 staff across four continents. It is the world's leading supplier of microwave and millimetre-wave electronic components used in the telecommunications and aerospace industries.

There is Filtronic technology in 75 per cent of Nokia mobile phones and the new generation of Eurofighter jets.

Few businesses were hurt quite as badly as Filtronic by the dramatic collapse in the value of telecommunications stocks in 2001. Within 12 months, the business saw its share price drop from £25 to 25p.

Much of the fall in confidence was due to speculative borrowing by other firms in the sector.

"It was a frustrating time to say the least," remarked Prof Rhodes. "I think that the company was overvalued at its peak, and I said so at the time, but when it hit the bottom it was absolutely ridiculous. I never dreamt it would go down that low."

When the price slumped to £4.35 per share, David and his son Julian were both so convinced the only way was up that they each bought £1 million worth of shares. Then it fell to 25 pence.

"You could say that cost the family a bit of money," said Prof Rhodes. "But so often the share price just bears no resemblance to what is actually happening at the company."

Despite the experience, Prof Rhodes denied floating the company in 1994 had been a mistake. After 44 million shares were made available on the London Stock Market, at £1.05 each, the firm was left with a £15 million war chest to pay for the new Saltaire HQ and a facility in the United States.

"At times, I regret starting the company because of all the problems that it has caused for both me and my family," he said. "20 years ago I had to put my house on the line to keep it going - people don't understand what the risks are.

"But I don't regret floating the business because that gave us the opportunity to expand and I could not have done that from the private business. Once you take that decision you have to live with what comes with that."

David Rhodes is at his happiest showing me round the extensive and hugely impressive facilities at Saltaire.

Highlight is the laboratory where some of the finest minds in the industry, gathered from all over the world, design microwave and semi-conductor technology so advanced that Prof Rhodes confidently proclaims: "No other firm can come even remotely close to us".

Prof Rhodes spent his formative years selling goods on Doncaster market and admits he could have had no better grounding in how business works.

As the firm has grown there has been plenty of wheeling and dealing. From America to Australia, via China and Finland, companies have been bought and sold, downsized and expanded.

The biggest gamble - although Prof Rhodes insists he's no gambler - came with the purchase of the former Fujitsu site in Newton Aycliffe.

Fujitsu, which operated the site as a silicon plant, had written-off £370 million there as a fall in the price of the product made it unprofitable.

Filtronic realised the site could be transformed into a mass production facility for integrated mobile phone products. The deal, at the height of the dot com boom in 1999, saw Filtronic's share price hit an all-time high.

But the investment soon became a noose around the company's neck. The huge site - renamed Filtronic Compound Semi-Conductors - possessed brilliant workers, but the product was too advanced for its time.

The £1 million per month operating cost of Newton Aycliffe became too much to bear but Prof Rhodes never accepted the purchase had been a mistake. "If somebody else bought that facility from scratch today, it would cost £500 million to set up," he said.

The plant is now one of Filtronic's real jewels. It has developed part of the new 3G mobile base station technology there and it is home to the defence systems technology which Prof Rhodes sees as a key part of Filtronic's future.

In 1980, Prof Rhodes had outgrown the South Leeds terraced unit he had leased to house his fledgling business. He got planning permission to build an electronics factory in the shadow of his old university. His application brought claims from a local councillor that Filtronic was building nuclear bombs.

The scheme was scrapped and instead Prof Rhodes eventually settled on two warehouse-style industrial units in Charlestown, Baildon.

He became good friends with Jonathan Silver, the man responsible for reviving Salts Mill, and the pair worked together on Filtronic's expansion of its HQ in the weeks before Jonathan's death.

His other major passion is Bradford City. He played a key role in dragging the club back from the brink of extinction last year, again putting his house on the line for the good of a business.

Now he lets his son Julian, the chief executive, negotiate the complicated path back into the black. He is full of admiration for what Julian and new chairman Gordon Gibb have achieved.

"Solving Bradford City's problems was like solving ten Newton Aycliffes in one," he said. "No one will ever know how bad things were there. I think what Julian has done has been phenomenal and I don't think that I could have achieved that."

Prof Rhodes will be 60 in October. But it's hard to imagine him walking away from the firm for some time yet.

"The important thing is that I can still do it," he said. "Most of my involvement is through developing theoretical concepts which can then be worked on in the laboratories."

With that, he produces from within the piles of paper on his desk a document entitled Output Universality In Maximum Efficiency Linear Power Amplifiers, taken from the International Journal of Circuit Theory and Applications.

It is the latest of about 100 articles and books he has written. The article is based around a concept which occurred to him as he lay on a Scilly Isles beach in 2000, basking in the glory of City's famous victory over Liverpool.

Not even David Weatherall's dramatic goal could compare with the buzz he got from working that one out.

"Doing something unique like that cannot compare with anything," he said.

"It is something that no-one has done before in the history of mankind. It is difficult to describe how it feels when you discover you have made a fundamental breakthrough."

For the brilliant professor, science will always win the day over business.