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POWI, Power Integrations
Power supplies, which convert the high-voltage AC from a wall outlet to the low-voltage DC required by most electronic devices.
We design, develop and market analog and mixed-signal integrated circuits ("ICs") and other electronic components and circuitry used in high-voltage power conversion.
Our products are used in power converters that convert electricity from a high-voltage source to the type of power required for a specified downstream use.
The business
What it sells, where the money comes from, the kind of company it is.
The business in brief
read the 10-K →What this business is and what moves its needle, from its own SEC filings.
- Situation
- Cyclical. Margins collapse and recover repeatedly across the record; a single year, good or bad, misstates the through-cycle earning power.
- What moves the needle
- Gross margin has run about 51% and operating margin about 13% through the cycle, a wide spread between price and the cost of what it sells — whether that advantage is durable pricing power or a margin that can erode is the question the record is for. The operating margin has swung widely — from 2.3% to 52% over the years — so the through-cycle figure carries more than any single year, and the worst year more than the best. Inventory runs near 21% of sales, so how fast it turns back into cash — and the risk of writing it down when demand softens — sits alongside the margin. Read this kind of business on process leadership and the capex cycle. On its own account, the filing leans hardest on customer concentration, set against the numbers in what the filing emphasizes, below.
- Is it a good business?
- Return on capital has sat near the cost of capital (median 11%). The steadier read is owner earnings: roughly 17% of revenue reaches owners as cash, consistently. The cycle and the balance sheet decide this one; the worst year tells more than the median, and the rest is in the 10-K.
Every line is arithmetic on the company's filings, shown in full in the sections below.
Where the money comes from
read the 10-K →Revenue spreads across 7 regions, the largest Hong Kong/China at 55%.
- Hong Kong/China55%$246M
- South Korea9%$40M
- Other8%$36M
- Germany6%$27M
- Taiwan6%$26M
- India5%$24M
- Other10%$46M
From the segment footnote of the company's own 10-K. Shares are of total revenue; the profit bar shows each segment's share of segment operating profit, before unallocated corporate costs.
The record
Ten years of arithmetic, read across the cycle.
The record, 2016–2025
realized figures from each filing · older years to the left| 2016’16 | 2017’17 | 2018’18 | 2019’19 | 2020’20 | 2021’21 | 2022’22 | 2023’23 | 2024’24 | 2025’25 | TTMTTMMar 2026 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Income statement | |||||||||||
| $390M | $432M | $416M | $421M | $488M | $703M | $651M | $445M | $419M | $444M | $446M | RevenueRevenue |
| 49% | 49% | 52% | 51% | 50% | 51% | 56% | 52% | 54% | 54% | 54% | Gross marginGross mgn |
| 8% | 8% | 9% | 9% | 8% | 6% | 4% | 7% | 9% | 10% | 9% | SG&A / revenueSG&A/rev |
| 16% | 16% | 17% | 17% | 17% | 12% | 14% | 22% | 24% | 23% | 23% | R&D / revenueR&D/rev |
| $49M | $58M | $56M | $217M | $70M | $175M | $180M | $35M | $18M | $10M | $5M | Operating incomeOp. inc. |
| 12.5% | 13.3% | 13.4% | 51.6% | 14.4% | 24.9% | 27.7% | 7.9% | 4.3% | 2.3% | 1.1% | Operating marginOp. mgn |
| $49M | $28M | $70M | $193M | $71M | $164M | $171M | $56M | $32M | $22M | $17M | Net incomeNet inc. |
| 2% | 54% | — | 13% | 5% | 7% | 7% | — | -5% | -5% | — | Effective tax rateTax rate |
| Cash flow & returns | |||||||||||
| $98M | $82M | $84M | $224M | $126M | $231M | $215M | $66M | $81M | $112M | $105M | Operating cash flowOp. cash |
| $17M | $18M | $19M | $19M | $24M | $31M | $35M | $35M | $33M | $27M | $26M | DepreciationDeprec. |
| $11M | $11M | ($27M) | ($12M) | ($192K) | ($3M) | ($13M) | ($54M) | ($19M) | $23M | $25M | Working capital & otherWC & other |
| $12M | $32M | $25M | $24M | $71M | $47M | $39M | $21M | $17M | $24M | $21M | CapexCapex |
| 3.1% | 7.5% | 5.9% | 5.7% | 14.5% | 6.7% | 6.0% | 4.7% | 4.1% | 5.5% | 4.6% | Capex / revenueCapex/rev |
| $86M | $50M | $59M | $200M | $55M | $184M | $176M | $45M | $64M | $87M | $85M | Owner earningsOwner earn. |
| 22.0% | 11.5% | 14.3% | 47.6% | 11.3% | 26.1% | 27.0% | 10.1% | 15.3% | 19.6% | 18.9% | Owner earnings marginOE mgn |
| $86M | $50M | $59M | $200M | $55M | $184M | $176M | $45M | $64M | $87M | $85M | Free cash flowFCF |
| 22.0% | 11.5% | 14.3% | 47.6% | 11.3% | 26.1% | 27.0% | 10.1% | 15.3% | 19.6% | 18.9% | Free cash flow marginFCF mgn |
| $0 | $0 | — | — | — | — | $0 | $0 | $10M | $0 | $0 | AcquisitionsAcquis. |
| $15M | $17M | $19M | $21M | $25M | $33M | $41M | $44M | $46M | $47M | $47M | Dividends paidDiv. paid |
| $6M | $9M | $103M | $7M | $3M | $74M | $311M | $55M | $28M | $98M | — | BuybacksBuybacks |
| 11% | 6% | 14% | 35% | 12% | 22% | 26% | 5% | 3% | 2% | 1% | ROICROIC |
| 10% | 5% | 13% | 27% | 9% | 18% | 23% | 7% | 4% | 3% | 2% | Return on equityROE |
| 7% | 2% | 10% | 24% | 6% | 14% | 17% | 2% | −2% | −4% | −5% | Retained to equityRetained/eq |
| Balance sheet | |||||||||||
| $250M | $283M | $229M | $411M | $449M | $530M | $354M | $312M | $300M | $250M | $257M | Cash & investmentsCash+inv |
| $7M | $17M | $11M | $24M | $36M | $41M | $21M | $15M | $27M | $18M | $14M | ReceivablesReceiv. |
| $53M | $57M | $81M | $90M | $103M | $99M | $135M | $163M | $166M | $167M | $163M | InventoryInvent. |
| $30M | $33M | $32M | $27M | $35M | $44M | $30M | $26M | $30M | $34M | $31M | Accounts payablePayables |
| $29M | $41M | $60M | $87M | $104M | $97M | $126M | $151M | $163M | $151M | $146M | Operating working capitalOper. WC |
| $318M | $365M | $332M | $541M | $601M | $687M | $525M | $512M | $514M | $458M | $458M | Current assetsCur. assets |
| $44M | $51M | $48M | $50M | $63M | $72M | $58M | $49M | $55M | $70M | $67M | Current liabilitiesCur. liab. |
| 7.2× | 7.1× | 6.9× | 10.7× | 9.6× | 9.5× | 9.0× | 10.5× | 9.3× | 6.5× | 6.9× | Current ratioCurr. ratio |
| $92M | $92M | $92M | $92M | $92M | $92M | $92M | $92M | $95M | $95M | $95M | GoodwillGoodwill |
| $554M | $621M | $589M | $804M | $903M | $1.0B | $840M | $820M | $829M | $772M | $771M | Total assetsAssets |
| ($250M) | ($283M) | ($229M) | ($411M) | ($449M) | ($530M) | ($354M) | ($312M) | ($300M) | ($250M) | ($257M) | Net debt / (cash)Net debt |
| $503M | $548M | $527M | $725M | $810M | $912M | $755M | $752M | $750M | $673M | $672M | Shareholders’ equityEquity |
| 5.4% | 5.7% | 5.2% | 5.5% | 6.3% | 5.3% | 3.4% | 6.4% | 8.4% | 8.9% | 8.4% | Stock comp / revenueSBC/rev |
| Per share | |||||||||||
| 59.2M | 61.1M | 60.3M | 59.6M | 60.8M | 61.5M | 58.4M | 57.6M | 57.1M | 56.3M | 55.9M | Shares out (diluted)Shares |
| $6.58 | $7.07 | $6.90 | $7.05 | $8.03 | $11.44 | $11.16 | $7.71 | $7.33 | $7.87 | $7.99 | Revenue / shareRev/sh |
| $0.83 | $0.45 | $1.16 | $3.24 | $1.17 | $2.67 | $2.93 | $0.97 | $0.56 | $0.39 | $0.30 | EPS (diluted)EPS |
| $1.45 | $0.81 | $0.98 | $3.36 | $0.90 | $2.99 | $3.02 | $0.78 | $1.12 | $1.55 | $1.51 | Owner earnings / shareOE/sh |
| $1.45 | $0.81 | $0.98 | $3.36 | $0.90 | $2.99 | $3.02 | $0.78 | $1.12 | $1.55 | $1.51 | Free cash flow / shareFCF/sh |
| $0.25 | $0.27 | $0.31 | $0.34 | $0.41 | $0.53 | $0.71 | $0.76 | $0.81 | $0.84 | $0.84 | Dividends / shareDiv/sh |
| $0.21 | $0.53 | $0.41 | $0.40 | $1.16 | $0.77 | $0.67 | $0.36 | $0.30 | $0.43 | $0.37 | Cap. spending / shareCapex/sh |
| $8.49 | $8.97 | $8.74 | $12.15 | $13.32 | $14.84 | $12.94 | $13.05 | $13.12 | $11.95 | $12.02 | Book value / shareBVPS |
Share counts before 2018 are restated ×2 for a stock split, so per-share figures sit on one basis.
| 9-yr | 5-yr | |
|---|---|---|
| Revenue / share | +2.0%/yr | −0.4%/yr |
| Owner earnings / share | +0.7%/yr | +11.3%/yr |
| EPS | −7.9%/yr | −19.6%/yr |
| Dividends / share | +14.2%/yr | +15.2%/yr |
| Capital spending / share | +8.6%/yr | −17.9%/yr |
| Book value / share | +3.9%/yr | −2.2%/yr |
The record, charted
FY2016–2025Each measure over its full record; the current point and the worst year marked. Share counts on the current split basis.
Owner earnings vs. net income
Owner earningsNet incomeThe accountant's number, and the cash an owner can take; the gap is the tell.
Where the cash went
ReinvestBuybacksDividendsAcquisitionsRetainedBeyond op. cashEach year's outlays against its operating cash: the mix, and how it drifts. The hatched cap is spending beyond that year's operating cash — financed from the balance sheet or borrowing, not operations.
Net income is the accountant's number; owner earnings is the cash an owner could take out. The walk between them, off the cash-flow statement, and whether the gap is widening or holding.
In fiscal 2025 the business turned $22M of profit into $87M of owner earnings: more cash than the profit line showed, after the non-cash charges and the capital it put back in.
| FY2025 | FY2024 | FY2023 | FY2022 | FY2021 | |
|---|---|---|---|---|---|
| Reported net income | $22M | $32M | $56M | $171M | $164M |
| Depreciation & amortizationnon-cash charge added back | +$27M | +$33M | +$35M | +$35M | +$31M |
| Stock-based compensationreal costnon-cash, but a real cost | +$40M | +$35M | +$29M | +$22M | +$38M |
| Working capital & othertiming of cash in and out, other non-cash items | +$23M | −$19M | −$54M | −$13M | −$3M |
| Cash from operations | $112M | $81M | $66M | $215M | $231M |
| Capital expenditurecash put back in to keep running and to grow | −$24M | −$17M | −$21M | −$39M | −$47M |
| Owner earnings | $87M | $64M | $45M | $176M | $184M |
| Owner-earnings marginowner earnings ÷ revenue | 20% | 15% | 10% | 27% | 26% |
Owner earnings is the cash an owner could pull out without starving the business: operating cash less the capital it must spend to hold its position . The cash-flow statement also adds stock comp back as non-cash, but it is a real cost paid in shares; counted as the expense it is (less $40M), owner earnings is nearer $47M.
Maintenance capex is estimated as depreciation where a growing business invests above it; free cash flow is the figure the scorecard's free-cash margin reads.
Quality & stewardship
Returns, the balance sheet, capital allocation, and pay.
Owner’s Scorecard
Will it survive?
- No meaningful interest burdenLittle or no interest expense reported
What this means
Little or no interest expense reported, the business isn't leaning on lenders to operate.
- Net cash, debt-freeCash $59M + ST investments $191M − debt $0
What this means
Cash and short-term investments exceed every dollar of debt by $250M, on net the company owes nothing, and can act from strength when others can't. Net debt is the leverage figure that matters: the cash is already set against the debt. Strategic or illiquid investments aren't counted here.
- Long (60+ days)DSO 15 + DIO 302 − DPO 61 days
What this means
Days cash is tied up between paying suppliers and collecting from customers. Lower is better; a long cycle means growth itself eats cash.
Is it a good business?
- Not enough dataIndustry peers: median 3%
What this means
The filing data didn't include the inputs for this check.
- High through the cycle10-yr median margin, range 10%–48%; latest $87M = operating cash $112M − maintenance capex $24MIndustry peers: median 14%
What this means
What an owner could take out without starving the business: operating cash less the maintenance capital it must spend to hold its position — Buffett's owner earnings. That's 20% of revenue this year, a 15% median across 10 years. Treating stock comp as the real expense it is (less $40M of SBC) leaves $47M.
- Cash-backedCash from ops $112M ÷ net income $22M
What this means
How much of reported profit showed up as operating cash. Above 1× is reassuring; well below suggests earnings lean on accruals. One year is noisy, growth and working-capital swings distort it, and this is operating cash, not free cash. Watch the multi-year trend.
How is the cash used?
- Returned more than it generatedDividends + buybacks $145M ÷ Owner Earnings $87M
What this means
The company returned more than it generated: against $87M of Owner Earnings, $145M (167%) went back to shareholders, $47M dividends, $98M buybacks — the excess came from the balance sheet or borrowing, not the year's operations. Net of $40M stock comp, the real buyback was about $58M. Sustained, that pattern draws down cash or adds debt; the net-debt line above shows where it stands.
- Investing or harvesting? 0.90×MaintainingCapex $24M ÷ depreciation $27M
What this means
Descriptive, not a grade. Above ~1× means investing faster than assets wear out (growth, or, sustained for years, today's earnings carrying less depreciation than tomorrow's will). Below means spending less than it's wearing out (efficiency, or a melting asset base). The ratio won't tell you which; the filings will.
Graham’s defensive tests · 3 of 5 met
Graham’s numerical criteria for the defensive investor (The Intelligent Investor, ch. 14), run on the filings. A floor of safety, not a buy signal; many fine modern businesses fail his strictest liquidity rules by design.
- Adequate size MissRevenue ≥ $2B · $444M
What this means
Big enough to weather a storm. Graham's 1972 floor was ~$100M of sales (≈ $700M today); we use a $2B revenue line as a conservative modern stand-in.
- Strong liquidity PassCurrent ratio ≥ 2× · 6.51×
What this means
Current assets at least twice current liabilities, near-term bills covered without touching the business. Strict by design: many cash-rich modern firms run leaner and miss it, holding their cushion in longer-dated securities.
- Earnings stability PassA profit every year (10-yr record) · no losses
What this means
Graham wanted earnings in each of the past ten years, the stability a defensive owner leans on.
- Dividend record PassUninterrupted dividends · paid every year (10)
What this means
An unbroken dividend was Graham's mark of durability. He wanted twenty years; the filings show about ten, and a single suspension breaks the streak. Non-payers, many fine modern compounders, fall outside his defensive net by design.
- Earnings growth MissEarnings +33% over the record · −25%
What this means
At least a third more earnings than a decade ago, averaging three years at each end. Net income (not per-share), so stock splits don't distort it, buybacks and dilution show up in the share-count line instead.
- Moderate price —P/E ≤ 15 and P/E × P/B ≤ 22.5 · decided by the price
What this means
Graham's valuation gate, the wall he kept between a sound business and a sound investment. Three-year average earnings are $0.66/share (latest year $0.40), the averaged base the calculator's gate runs on, and book value is $12.08/share. Enter a price in “What the price implies” just below for the P/E, P/B, and whether it clears. But this is the rule Buffett outgrew: there's no hard P/E law, and a wonderful business can deserve a far richer multiple if the thesis holds, treat it as the bargain-hunter's floor, not a verdict on the price.
Durability & moat, 2016–2025
Whether the record’s returns held, and what the capital reinvested earned.
- Profitable years 10 of 10
What this means
Never lost money over the record, the earnings stability Graham insisted on.
- Operating margin 13% → 5% (3-yr avg ends)
In the filing’s words The words explain the slip: the filing names price competition rather than pricing actions of its own — a business that looks to take its price, not set it.
What this means
Through the cycle the operating margin slipped — about 13% early to 5% lately, median 13% — competition or costs are biting in.
- Owner earnings growth +1%/yr
What this means
Owner earnings grew about 1% a year over the record.
- Worst year 2025 · 2.3% op. margin
What this means
Stayed profitable even in its hardest year, the resilience that survives recessions.
- Dividend record rising
What this means
Paid and raised the dividend across the record, the continuity Graham prized.
Does AI threaten the moat?
Low contestabilityThe moat is physical, regulated or balance-sheet-funded, the kind AI cuts costs within but does not contest.
Its FY2025 10-K names artificial intelligence as a competitive threat, in language that was not in the prior year's filing.
“These markets may also not develop as anticipated if AI training and inference costs drop materially due to customer adoption of less expensive alternative technologies or approaches, or if customers achieve desired performance using alternative solutions that reduce the need for certain components.…”
AI is unlikely to contest a moat that is physical, regulated or balance-sheet-funded; here it reads more as a cost tool than a threat.
Read from the filing's own risk factors, paired with the industry's structure under its SIC code; the durability is read above, the price below.
All figures as filed; the source filing is linked above.
Current Position
as of the latest quarter, Mar 31, 2026Can the business pay what it owes this year, off the freshest balance sheet: the quality of the assets, the debt actually coming due, and what a low ratio means here.
- Cash & short-term investments$257M
- Receivables$14M
- Inventory$163M
- Other current assets$24M
- Accounts payable$31M
- Other current liabilities$35M
From the company's latest filing.
How the cash was used, 2016–2025
Over the record, the business generated $1.3B of operating cash; how management split it reads as a cash returner, paying most of what it earns straight back to owners.
- Reinvested$313M · 24%
- Dividends$307M · 23%
- Buybacks$695M · 53%
- Retained (debt / cash)$3M · 0%
- Returned to owners$1.0B
100% of the owner earnings the business produced over the span, $307M as dividends and $695M as buybacks.
- Average price paid for buybacks—
Buybacks ran $695M over the span, but the filings don't tag the share count needed to deduce the average price paid.
- Net change in share count−5.7%
The diluted count fell from 59M to 56M, so the buybacks outran the stock issued to staff.
- Dividend record$0.84/sh
Paid in 10 of the years on record, the per-share dividend growing about 14% a year. It was never cut over the span.
Buybacks are gross of stock issued to staff; the share-count line above is the net of that, the figure that decides whether owners gained. The average price paid blends a year of purchases (and any accelerated repurchase), so it is close, not exact. The record of where the cash went and on what terms.
Management, ownership & pay
read the proxy →From the proxy: how much of the business the people running it own, and how they are paid, beside what the business earned for its owners in the same years.
| Fiscal year | Pay, as filed | “Actually paid” | Owner earnings |
|---|---|---|---|
| 2021 | $6.6M | $16.7M | $184M |
| 2022 | $7.0M | −$13.1M | $176M |
| 2023 | $8.2M | $6.8M | $45M |
| 2024 | $8.6M | $8.8M | $64M |
| 2025 | $8.2M | −$839k | $87M |
| 2025 | $6.3M | $6.0M | $87M |
Both pay figures are the company’s own, from the pay-versus-performance table its proxy statement files. “As filed” is the Summary Compensation Table total: salary, bonus, and equity awards at their value on the day of grant. “Actually paid” is the SEC’s prescribed recalculation, which re-marks those equity awards to what they became as they vested; it can swing far above or below the filed figure in either direction, and negative years occur. Owner earnings are the whole business's, from the record above, for the same fiscal years.
- Insider ownership1.2%
The stake all directors and executive officers hold together, per the 2026 proxy: skin in the game, the first thing Munger reads.
- CEO pay ratio75:1
What the chief earns for every dollar the median employee makes, per the 2026 proxy. A high ratio alone settles nothing; some businesses are genuinely top-heavy in scarce skill. A runaway figure is where Buffett starts asking whether the board is doing its job.
- Stock-based compensation$40M
The slice of the business handed to employees in shares this year, 9% of revenue, equal to 389% of operating profit. Buffett's oldest accounting fight: this is compensation, compensation is an expense, real whether or not the headline earnings admit it. One trap: the cash-flow statement adds SBC back, so the operating cash, and the owner earnings drawn from it, are flattered by exactly this amount; counted as the cost it is, what an owner keeps is lower.
Inverting the record
Invert: instead of why Power Integrations is a good business, the question is what would make owning it a mistake, and whether those marks are in the record. Disconfirming tests across 2016–2025.
1 of the 4 tests turned up something to look into; the other 3 came back clean.
- Look hereDid receivables and inventory outpace sales?15% → 40% of sales
Receivables and inventory grew from $59M to $177M while revenue grew 15%: working capital is climbing faster than sales (15% of revenue then, 40% now). That can mean customers paying slower, stock building up, or revenue pulled forward. The filing's cash-flow and receivables notes say which.
- Is it less profitable than it was?
- Did the share count rise anyway?
- Did reported profit become cash?
Each test is read from the filings and is noisy alone; a flag can mark a cyclical trough or a year of heavy investment as easily as a problem. The filing says which.
What an owner would ask, FY2025
read the 10-K →- How much of the revenue rides on one buyer?≈$361M · 81% of revenue on the largest customers (TTM)
“Our top ten customers, including distributors that resell to OEMs and merchant power supply manufacturers, accounted for approximately 81%, 79% and 80% of net revenue in 2025, 2024 and 2023, respectively.”verify →
The questions the record and the charts do not answer on their own; each carries the figure and the place to look.
Peers, Semiconductors
The same industry, side by side on owner economics. Each figure is a through-cycle median, so a peak or trough year can’t distort it; the group median at the foot is the line to read each against.
| Company | Revenue | Gross margin | Op. margin | ROIC | Owner earn. margin |
|---|---|---|---|---|---|
| AOSLAlpha and Omega Semiconductor Limited | $696M | 26% | 2.6% | 3% | 2% |
| KLICKulicke and Soffa Industries Inc. | $654M | 47% | 9.4% | 8% | 14% |
| LSCCLattice Semiconductor | $523M | 60% | 9.1% | 9% | 22% |
| SHLSShoals Technologies Group Inc. | $475M | 36% | 17.0% | 10% | 17% |
| MXLMaxLinear Inc. | $468M | 55% | -5.3% | -3% | 15% |
| POWIPower Integrations | $444M | 51% | 13.4% | 11% | 17% |
| SKYTSkyWater Technology Inc. | $442M | 16% | -6.2% | -14% | -12% |
| AMBAAmbarella | $391M | 61% | -21.4% | -15% | 11% |
| Group median | — | 49% | 5.8% | 6% | 14% |
The price
What a price has to assume.
What the price implies
reverse-DCFType today's close and see the owner-earnings growth you'd have to believe to justify it, beside what Power Integrations has delivered.
Through the cycle, Power Integrations earns about $77M on its 17.4% median owner-earnings margin. This year’s 19.6% margin runs in line with that. Normalize, below, values the price on that through-cycle figure rather than the latest year.
—
9.0% = the 4.55% 10-year Treasury (Jul 15, 2026) + 4.45 points of equity premium. The rate you require is yours to set.
Enter a price above to run it.
A dated snapshot of the price you typed, the assumptions you set, and what the page showed for them. A snapshot is never edited after it is saved. Your notebook is yours alone — the commitment states what is stored and what we will never do.
Graham capped the multiple at 15×; Buffett and Munger let that rule go: a wonderful business can deserve 50× if the thesis holds. The gate marks the bargain-hunter's floor.
Prefilled with the 10-year Treasury (4.55%, as of Jul 15, 2026). Edit it for today’s exact figure, or a AAA corporate yield.
Graham measured a stock against the bond you could own instead, the heart of his margin of safety. Enter a price above to weigh the owner-earnings yield against this bond.
Owner earnings $85M on 56M shares outstanding, per the 10-Q cover, as of 2026-05-04; net cash $257M. The base is the latest year by default; Normalize values it on the through-cycle median owner-earnings margin (to avoid paying on a peak year). Net of stock comp treats option pay as the expense it is. The dials set the multiple a growth belief justifies; the price, and every dollar on this page, is yours.
Manual order: ← POST its page in the Manual POWL →
Industry order: ← POET the Semiconductors chapter Q →