Commonwealth Bank of Australia (ASX: CBA) shares have long been popular with passive income investors for the bank's lengthy track record of paying two fully franked dividends per year.

Atop that welcome passive income, shares in the S&P/ASX 200 Index (ASX: XJO) bank stock have surged 44.1% over the past year, and 152.4% over five years.

Shares are down 1.9% in intraday trade on Thursday, changing hands for $180.27 apiece.

Now, you're unlikely to hear stockholders complain about the big longer-term gains delivered by CBA shares. But this does mean that the modest annual increases in the CBA dividends over the past five years have led to materially lower yields for investors buying at recent prices.

Here's what I mean.

CommBank paid out a final fully franked dividend of $2.50 a share on 27 September and an interim dividend of $2.25 on 28 March.

That works out to a full year passive income payout of $4.75 a share.

At the current CBA share price of $180.27, this equates to a fully franked trailing dividend yield of 2.6%.

But some investors will be earning much more on their shares.

Buying the dip on CBA shares to turbocharge that passive income

Whenever you see quality ASX 200 dividend stocks like CommBank trading at seemingly bargain-level prices, it could represent an opportune time to buy shares to build up a boosted, longer-term passive income stream.

Now, I'm not talking about trying to time the market and get in at the very top or bottom of a company's share price. That's almost impossible, certainly not consistently.

But in the months following the COVID market meltdown in 2020, there were myriad bargains to be had on the ASX.

For example, on 2 October 2020, CBA shares closed the day trading for $63.78 each. Investors may have been encouraged to buy that day, with the ASX 200 bank stock having recovered from lows of less than $60 per share in mid-May that year. So, we're not entirely cherry picking the dates here.

Now, let's say you waded in on the day and bought into Australia's biggest bank stock for $63.78 a share.

Assuming you held onto those shares, you'd still have received the $4.75 a share in fully franked CBA dividends over the past 12 months. And that would see you earning a 7.5% dividend yield on the shares you bought in October 2020.

Atop that boosted passive income, you'd also have booked a 182.6% capital gain on those CBA shares at current prices. Not to mention the six other dividend payouts you'd have received over the years.