With interest rates and inflation running high, it's perhaps never been more important to hold stocks that pay not just dividends, but rising dividends.

Given the beating the broader semiconductor sector has taken, a great opportunity has opened up in two defensive chip names that should not only survive any downturn, but actually grow their dividends through it, leading to years of rising passive income for their investors.

Texas Instruments

Texas Instruments (TXN 1.44%) has some of the more compelling characteristics for the defensive dividend investor. The company designs and manufactures a large portfolio of analog and embedded chips, with a diverse customer base and structurally low manufacturing costs, ensuring high margins.

Over the past decade, TI has targeted the industrial and automotive chip sectors, given that autos and factories will become more automated and use more chips per unit each and every year. That's looking like a good bet these days, as those end markets still appear strong, even though consumer electronics markets are in decline in 2022. Since 2013, Texas Instruments' auto and industrial exposure has risen from 42% to 62% of revenue.

Texas Instruments currently yields 3.1%, but that yield has grown at a stunning 21% annualized rate from 2004 to 2021. During that time, free cash flow per share has grown 12% annually and shares outstanding were reduced 46%.

In September, TI announced another 8% dividend increase. That may seem underwhelming given its past; however, the company is embarking on a higher investment period over the next three years, which will greatly expand capacity to support a near-doubling of revenue through the end of the decade.

In any case, TI has held up relatively well this year, only down slightly, while the broader chip index is down nearly 40%. That outperformance shows the faith investors have in this blue chip company's sustainable profit growth.

Broadcom

Another defensive chip name is Broadcom (AVGO -4.38%), which currently yields 3.6%, and also comes with a history of dividend growth. In fact, Broadcom has increased its dividend by a whopping 43% annualized rate between 2016 and 2022, increasing the payout nearly eight and half times over.

Under CEO Hock Tan, Broadcom has grown via acquisitions, which management then folds into Broadcom's corporate infrastructure and sales force, expanding margins.

After diversifying its chip portfolio, mostly across enterprise and industrial applications, management interestingly began acquiring software companies, with the acquisitions of CA Technologies in 2018 and Symantec in 2019. Most recently, Broadcom made an offer to buy VMWare (VMW), its biggest acquisition yet, for $61 billion in cash and stock.

The software segment brings in recurring subscription revenue, which helps even out the fluctuations in the more cyclical semiconductor segment. Since Broadcom has a lot of enterprise exposure, it can also bundle its infrastructure, security, and private cloud software with corresponding chips.

Still, even Broadcom's semiconductor portfolio appears resilient in the face of this economic slowdown. Broadcom beat revenue and earnings expectations last quarter and even saw its backlog grow to $31 billion -- nearly one year of revenue. Its semiconductor revenues grew 29% fueling overall revenue growth of 23%.

That could be because Broadcom makes a variety of chips for networking, enterprise and industrial customers, which seem to be more in-demand than consumer electronic chips today. Even though Broadcom has wireless exposure, its big client is Apple, which seems to be faring much better than other handset makers in this environment.

In any case, Broadcom management clearly knows how to target desirable markets, make acquisitions, and expand margins over time. That should fuel continued dividend growth for years to come.