Category: 3. Business

A rise in the number of sweet, food-scented perfumes on the market could be linked to an increase in the use of weight-loss medication, according to the market research firm Mintel.

Food-inspired fragrances, with scent profiles that feature vanilla, coffee and caramel and referred to in the industry as “gourmand” perfumes, have surged in popularity in the past three years. Launches of sugary-scented, desert-themed fragrances increased by 24% last year alone, Mintel said.

The rise in popularity is happening alongside the increased use of GLP-1 medications for weight loss, such as Ozempic, Wegovy and Mounjaro.

“Fragrance brands may increasingly explore such notes to address GLP-1-driven appetite suppression,” said Clotilde Drapé, a global beauty analyst at Mintel, as consumers “strive to stay lean while enjoying decadent, food-inspired scents”.

Mintel’s Future of Fragrance 2025 report predicts a further resurgence in sweet scents, tied to increased weight-loss medication use. “Online discussions have linked GLP-1 medications to changes in appetite and sensory experiences, potentially driving interest in sensory stimulation like fragrances,” Drapé said.

Gourmand perfumes are trending heavily among younger consumers online. Google and TikTok searches for “gourmand fragrances” have shown year on year growth of +170% in the US since 2023, according to the New York-based consumer research firm Spate.

In April the singer, songwriter and actor Sabrina Carpenter released the fragrance Me Espresso, the latest addition to her gourmand-centred perfume line. It is described as a sugary iced coffee in olfactory form, with notes of espresso, biscuit and whipped cream. The Fragrance by Sabrina scents also include Sweet Tooth, Caramel Dream and Cherry Baby and are all shaped like chocolate bars, adding to the dessert-themed experience.

“Generally speaking, it’s a gen Z-inspired fragrance trend,” said Amanda Carr, a fragrance writer at the website We Wear Perfume.

For younger generations, with recently acquired spending power, gourmand is an accessible gateway into the perfume market. “It’s like a baked cake or a sweet treat. It’s very easy for somebody who’s new to fragrance to understand it,” says Carr.

“Vanilla does hang about, it’s a very heavyweight note. So it seems like a good value for money fragrance, and that appeals to gen Z as well.”

The global fragrance market continues to boom, with an expected annual growth of 3.3% in 2025, according to the data company Statista.

Popular trends shared on TikTok include “scent layering”, which involves buying multiple scented body care products, from body oil to lotions, to boost the longevity of the fragrance.

Drapé said “mood-boosting” is the top reason for using fragrance in the UK, driving the popularity of sweet scents that are linked with indulgence.

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ISLAMABAD – UK Pound buying rate dropped to Rs377.93 in open market of Pakistan on Saturday after a decline of Rs1.81.

The selling rate for the Pound also slipped and stood at Rs378.6, according to the currency exchange association.

Overseas Pakistanis living in the UK closely monitor the currency exchange rates as they send significant remittances to Pakistan every month to support their families.

Remittances from the United Kingdom amounted to $450.4 million during July 2025, down by 16 percent compared to $537.6 million in June 2025. YoY inflows from the UK improved by 2 percent.

Overalls, the inflow of overseas workers’ remittances into Pakistan has recorded at $3.2 billion in July 2025.

According to the State Bank of Pakistan (SBP) data, remittances have surged by 7.4 percent to $3.2 billion in July this year compared to $3 billion in the same month of the previous year. On a monthly basis, remittances dipped by six percent, compared to $3.4 billion in June.

Investors and business leaders closely monitor currency fluctuations to manage financial risk and shape their strategic decisions.

Exchange rates also serve as key indicators of a country’s economic health and stability. In some cases, central banks intervene to influence currency values as part of broader economic policy measures.

Pakistan and the United Kingdom maintain a long-established economic relationship, built on mutual trade, investment, and collaborative development efforts.

Gold Rates in Pakistan Today, 19 August 2025

The Suzuki Alto, one of Pakistan’s top-selling compact vehicles, experienced a major drop in sales last month. According to data from the Pakistan Automotive Manufacturers Association (PAMA), sales plummeted by 75%, falling from 9,497 units in June to just 2,327 in July.

The steep decline followed recent government changes to taxation. The General Sales Tax (GST) on cars up to 850cc was raised from 12.5% to 18%. Additionally, the government introduced a new NEV levy, applying 1% to vehicles up to 1300cc, 2% for 1301cc to 1800cc, and 3% for larger vehicles. The Alto, although below 850cc, was still impacted by these fiscal adjustments.

Reacting to the tax changes, Pakistan Suzuki Motors Company (PSMC) raised the price of the Alto to Rs. 3,326,450. The higher price point pushed the car out of reach for many budget-conscious buyers, particularly first-time car owners, a segment that traditionally makes up a significant portion of Alto’s customer base.

In an attempt to shield buyers from the tax hike, PSMC adopted an early invoicing approach in June, processing orders for July and August in advance. While this strategy boosted June’s numbers, it contributed to a significant decline in subsequent months.

Adidas executives visited a small Indigenous town in the mountains of southern Mexico on Thursday to offer an apology over a sandal-inspired shoe design that Mexico’s government had blasted as cultural appropriation.

The German sportswear company sent representatives from its Mexican unit to Villa Hidalgo Yalalag, a town in Oaxaca state, to deliver the comments in person after issuing a written apology last week.

The issue related to the Oaxaca Slip On, designed by Mexican-American designer Willy Chavarria, which locals say closely resembles their traditional handmade huarache sandals.

“We understand this situation may have caused discomfort, and for that reason, we offer a public apology,” Karen Gonzalez, head of Legal and Compliance at Adidas Mexico, told a few dozen people gathered at an outdoor sports field.

The event included traditional music and attendees in Indigenous attire.
Gonzalez said Adidas would in future seek collaboration with Villa Hidalgo Yalalag to ensure respect for its cultural heritage. The community is home to fewer than 2,000 people.

“Thank you very much for keeping your word,” said Mayor Eric Fabian. “(Our cultural heritage) is something we safeguard very carefully. Yalalag lives from its crafts,” he added.

The controversy drew national attention earlier this month when Mexican President Claudia Sheinbaum criticised Adidas and announced plans to explore legal avenues to protect Indigenous communities from alleged cultural appropriation by big companies.

Mexico has previously accused other big-name global fashion players of exploiting Indigenous designs without consent.

This study fills an existing gap by exploring the use of ChatGPT in the field of medical image-based questions and case-based teaching scenarios. Our findings demonstrate that ChatGPT exhibit the capability to accurately answer image-based medical questions, with the GPT-4o version demonstrating a numerically higher accuracy. Prompt engineering enables ChatGPT to assist in the design of lesson plans, showcasing significant potential in medical education. Nevertheless, human verification and correction remain essential. These findings may serve as a significant step toward expanding the practical use of advanced ChatGPT versions, which have already demonstrated great potential in medical fields.

Previous studies have widely assessed the performance of ChatGPT on medical questions, predominantly utilizing earlier versions such as GPT-3.5 and GPT-4, which yielded inconsistent accuracy levels [1, 3, 4, 13,14,15, 17, 26, 27]. However, these studies excluded image-based questions due to the limitations of earlier versions, hindering potentials of ChatGPT in real-world teaching contexts. In response, our study specifically targeted medical image-based questions to fill this gap. The accuracy of ChatGPT in our findings is consistent with previous studies [14,15,16,17], while the higher version, GPT-4o, exhibited greater accuracy (nearly 90%) [18]. While GPT-4o demonstrated higher accuracy than GPT-4 across the image-based items, this difference did not reach statistical significance, likely due to the limited sample size. Nonetheless, the consistent directional trend aligns with recent findings on the evolving capabilities of multimodal LLMs, and supports further investigation in larger-scale evaluations.

In addition to evaluating model performance, our findings highlight broader implications for the application of large vision-language models (LVLMs) in medical education—particularly in the areas of assessment design and instructional content development. LVLMs such as GPT-4o may assist in generating multiple-choice questions from image-based course materials, offering opportunities to streamline item development. Furthermore, our study demonstrates that GPT-4o possesses a notable capacity for logical reasoning and analytical processing when evaluating incorrect answers, suggesting its potential utility in developing explanations that reinforce clinical thinking frameworks. However, ensuring the clinical validity, cognitive appropriateness, and pedagogical alignment of AI-generated content remains a critical challenge, underscoring the need for expert oversight. While this study focused on interpreting images embedded within question stems, future work could explore more complex formats in which answer options themselves are visual (e.g., electrocardiogram tracings or radiographs). These tasks require fine-grained image discrimination and multimodal reasoning, areas in which current models still face limitations. As such, advancing the visual acuity and contextual understanding of LVLMs is essential to support their integration into high-stakes assessment environments.

Beyond assessment, LVLMs like ChatGPT show promise as instructional aids in case-based teaching. As demonstrated in exploratory prompts (Appendix 1 and 2), the model can support educators in structuring lessons around specific clinical concepts and generating adaptive instructional feedback [27, 28]. With its ability to present information logically and adjust content to learner needs, ChatGPT may enhance personalized learning and curricular efficiency [5, 28, 29]. Our findings, in conjunction with prior research [30, 31], support the growing interest in AI-assisted pedagogy. Nonetheless, limitations persist. While GPT-4o exhibits high coherence and insight in reasoning tasks, errors remain—particularly in nuanced clinical contexts involving medical images. These inaccuracies underscore the importance of human oversight and expert validation to ensure instructional reliability and clinical relevance [27, 32,33,34,35]. As such tools continue to evolve, their optimal use will likely depend on integration with faculty-led review and revision mechanisms, ensuring safety, accuracy, and pedagogical value in medical education.

This study has several limitations. First, all model responses were generated via the ChatGPT web interface under default settings rather than through the OpenAI Application Programming Interface (API). Although personalization was disabled and each question was submitted in a newly initiated session to minimize memory effects, API-based deployment would allow for greater control over system parameters and eliminate potential user-specific variability. Second, each question was evaluated only once per model. This approach, consistent with prior LLM evaluation studies, minimized contextual contamination from repeated prompts—particularly relevant in session-based environments—but precluded assessment of intra-model variability. Future studies should consider multi-sample testing under controlled API conditions to examine response stability and reproducibility. Third, the relatively small number of publicly available USMLE-style questions with image content (n = 38) limited the statistical power and generalizability of the findings. Expanding the question pool and including a broader range of visual modalities—such as radiographs and electrocardiograms—would enhance benchmarking rigor. Fourth, the study did not isolate the respective contributions of visual versus textual inputs to model performance. While examples in the Supplementary Appendix suggest engagement with image content, dedicated experimental designs are needed to disentangle multimodal reasoning pathways and assess their relative influence. Finally, the study focused exclusively on GPT-4 and GPT-4o, which were the most accessible and stable vision-capable models at the time of evaluation (late 2024 to early 2025). Comparative studies involving other LVLMs, such as Gemini, LLaVA, or DeepSeek, are warranted to explore model-specific strengths and inform future applications in medical education.

WASHINGTON — Now that Federal Reserve Chair Jerome Powell has signaled that the central bank could soon cut its key interest rate, he faces a new challenge: how to do it without seeming to cave to the White House’s demands.

For months, Powell has largely ignored President Donald Trump’s constant hectoring that he reduce borrowing costs. Yet on Friday, in a highly-anticipated speech, Powell suggested that the Fed could take such a step as soon as its next meeting in September.

It will be a fraught decision for the Fed, which must weigh it against persistent inflation and an economy that could also improve in the second half of this year. Both trends, if they occur, could make a cut look premature.

Trump has urged Powell to slash rates, arguing there is “no inflation” and saying that a cut would lower the government’s interest payments on its $37 trillion in debt.

Powell, on the other hand, has suggested that a rate cut is likely for reasons quite different than Trump’s: He is worried that the economy is weakening. His remarks on Friday at an economic symposium in Grand Teton National Park in Wyoming also indicated that the Fed will move carefully and cut rates at a much slower pace than Trump wants.

Powell pointed to economic growth that “has slowed notably in the first half of this year,” to an annual rate of 1.2%, down from 2.5% last year. There has also been a “marked slowing” in the demand for workers, he added, which threatens to raise unemployment.

Still, Powell said that tariffs have started to lift the price of goods and could continue to push inflation higher, a possibility Fed officials will closely monitor and that will make them cautious about additional rate cuts.

The Fed’s key short-term interest rate, which influences other borrowing costs for things like mortgages and auto loans, is currently 4.3%. Trump has called for it to be cut as low as 1% — a level no Fed official supports.

However the Fed moves forward, it will likely do so while continuing to assert its longstanding independence. A politically independent central bank is considered by most economists as critical to preventing inflation, because it can take steps — such as raising interest rates to cool the economy and combat inflation — that are harder for elected officials to do.

There are 19 members of the Fed’s interest-rate setting committee, 12 of whom vote on rate decisions. One of them, Beth Hammack, president of the Federal Reserve’s Cleveland branch, said Friday in an interview with The Associated Press that she is committed to the Fed’s independence.

“I’m laser focused … on ensuring that I can deliver good outcomes for the for the public, and I try to tune out all the other noise,” she said.

She remains concerned that the Fed still needs to fight stubborn inflation, a view shared by several colleagues.

“Inflation is too high and it’s been trending in the wrong direction,” Hammack said. “Right now I see us moving away from our goals on the inflation side.”

Powell himself did not discuss the Fed’s independence during his speech in Wyoming, where he received a standing ovation by the assembled academics, economists, and central bank officials from around the world. But Adam Posen, president of the Peterson Institute for International Economics, said that was likely a deliberate choice and intended, ironically, to demonstrate the Fed’s independence.

“The not talking about independence was a way of trying as best they could to signal we’re getting on with the business,” Posen said. “We’re still having a civilized internal discussion about the merits of the issue. And even if it pleases the president, we’re going to make the right call.”

It was against that backdrop that Trump intensified his own pressure campaign against another top Fed official.

Trump said he would fire Fed Governor Lisa Cook if she did not step down from her position. Bill Pulte, a Trump appointee to head the agency that regulates mortgage giants Fannie Mae and Freddie Mac, alleged Wednesday that Cook committed mortgage fraud when she bought two properties in 2021. She has not been charged.

Cook has said she would not be “bullied” into giving up her position. She declined Friday to comment on Trump’s threat.

If Cook is somehow removed, that would give Trump an opportunity to put a loyalist on the Fed’s governing board. Members of the board vote on all interest rate decisions. He has already nominated a top White House economist, Stephen Miran, to replace former governor Adriana Kugler, who stepped down Aug. 1.

Trump had previously threatened to fire Powell, but hasn’t done so. Trump appointed Powell in late 2017. His term as chair ends in about nine months.

Powell is no stranger to Trump’s attacks. Michael Strain, director of economic policy studies at the American Enterprise Institute, noted that the president also went after him in 2018 for raising interest rates, but that didn’t stop Powell.

“The president has a long history of applying pressure to Chairman Powell,” Strain said. “And Chairman Powell has a long history of resisting that pressure. So it would be odd, I think, if on his way out the door, he caved for the first time.”

Still, Strain thinks that Powell is overestimating the risk that the economy will weaken further and push unemployment higher. If inflation worsens while hiring continues, that could force the Fed to potentially reverse course and increase rates again next year.

“That would do further damage to the Fed’s credibility around maintaining low and stable price inflation,” he said.

The detailed operation of conventional Bandgap Reference (BGR) Core circuits, including the Current Mirror BGR (CM-BGR) and the Cascaded Current Mirror BGR (Cascaded CM-BGR), is discussed in this section. These architectures are analyzed in terms of their temperature compensation mechanisms, process variation tolerance.

Conventional BGR core

Integrated circuits (ICs) must operate reliably in harsh environmental conditions, ranging from hot desert temperatures to sub-zero polar temperatures. To operate stably under such conditions, a Bandgap Voltage Reference (BGR) Core has been designed to generate a temperature-independent reference voltage, as shown in Fig. 1. The BGR circuit is essential to maintain stable operation by demonstrating process independence, stable operation over different semiconductor fabrication processes, voltage independence, minimizing variations due to supply fluctuations, and temperature independence, to operate reliably over a broad temperature range, usually from − 40 to + 125 °C¹⁴. The basic principle behind a BGR circuit is the generation of two voltages with opposite temperature coefficients to attain thermal stability. One such voltage is the Complementary to Absolute Temperature (CTAT) voltage, derived from the base-emitter voltage (V_BE) of a bipolar junction transistor (BJT). The V_BE voltage is of negative temperature coefficient, reducing by about − 2 mV/°C with a rise in temperature¹⁵. This CTAT voltage, from a diode-connected BJT, forms the foundation for temperature compensation in BGR circuits to provide a stable reference voltage over changing environmental conditions¹⁶.

So, V_BE is negative temperature co-efficient (− 2mv/°C).

The second one is PTAT Voltage (Proportional to Absolute Temperature). Derived from the thermal voltage (V_T = kT/q), which increases linearly with temperature at a rate of approximately + 0.087 mV/°C. By scaling this voltage appropriately, its temperature coefficient can be matched to that of VBE. A PTAT voltage generator achieved by subtracting the VBE of two BJTs operating with a current density ratio N⁷.

So, V_T is positive temperature co-efficient 0.087mv/°C)

The sum of these voltages, appropriately weighted, yields a temperature-independent reference voltage.

The output reference voltage is given by.

VREF = VBE + V_T⋅ln (N) = constant, which independent of PVT variations (when slope of CTAT = PTAT).

where ln (N) is a scaling factor determined by the ratio of slopes(m = 2/0.087 = 23). So, N should be very large in millions of transistors should be connected in the 2^nd stage.

Robust cascaded current mirror-based Bandgap Reference (BGR) circuits

A conventional current mirror and a stable cascaded current mirror-based BGR circuit are analysed in this section for improving stability against variations of Process, Voltage, and Temperature (PVT)^13,14,15. A single-stage BGR circuit based on current mirrors can be seen in Fig. 2a. The circuit consists of a PMOS current mirror (M1-M2) and a transistor-based BGR core (Q1-Q5). Temperature compensation is achieved by combining proportional-to-absolute-temperature (PTAT) and complementary-to-absolute-temperature (CTAT) voltages through the resistor R_BGR.

The cascaded current mirror-based BGR¹⁷ with its robust structure shown in Fig. 2c is comprised of two additional current mirror stages (M11-M22 and M33-M44) to achieve better current replication. As a result, the output reference voltage (V_BGROUT2) has enhanced immunity to supply variations.

Figure 2b, d illustrate the impact of R_BGR variation on V_BGROUT1 and V_BGROUT2. Similarly, the Single-stage current mirror and the Cascaded current mirror have linear relationships between V_BGR and R_BGR with varying sensitivity slopes, at 37.236 μV/Ω and 42.246 μV/Ω, respectively¹². Due to the greater slope obtained in the cascaded current mirror structure, it may be possible to obtain proportional to absolute temperature compensation (PTAT) for smaller R_BGR values.

The stability of BGR across an operating temperature range is shown through Fig. 2b, d. Figure 2e also shows how V_{BGR_OUT1} and V_{BGR_OUT2} with varying supplies (V_DD) compared to each other. A stable bandgap reference (BGR) topology, by virtue of using cascaded current mirrors, has less sensitivity to the supply voltage noise. Supply voltage is changed from 0 to 4 V, simulations are carried at various process corners as well as over a − 40 °C and 125 °C temperature range making use of the 65 nm CMOS process.

Figure 3 shows the effect of startup resistance variations on the BGR circuit output and the startup transistor biasing characteristic^13,16. In Fig. 3a, the BGR output voltage (V_BGROUT1) is studied versus various startup resistance (Rs) values. For lower Rs values (regions S1 and S2), the output is shifted away from the expected value and remains at around 3.2 V, which shows proper startup functioning, due to improper biasing of NM4. Thus, it is operated in a linear region as given in Fig. 3c. Nevertheless, as Rs increases above a critical value (around 20kΩ), the BGR output begins producing a constant 1.3 V (from Fig. 3b) (regions S3 to S5), which indicates that the startup circuit successfully biases the BGR properly at high resistance values, when NM4 is biased to run in the saturation region. Figure 3c shows the biasing voltage (V_GS) of the startup transistor NM4 versus different Rs values. At the beginning, NM4 is in the linear and saturation regions, allowing proper circuit startup. However, as Rs increases above a certain value, NM4 switches to the cutoff region, disabling the startup circuit and causing startup failure. This analysis verifies that choosing an optimum startup resistance is crucial in ensuring reliable BGR operation.

As shown in Fig. 4a, without the startup circuit, BGR fails to initialize correctly and stays in a metastable state, while with the startup circuit, it reaches the correct operating voltage of 1.3 V, as shown in Fig. 4b. A startup circuit is required to pull a small current at the beginning of operation in order to force the BGR into its correct operational state in Fig. 4c. Once the startup circuit is turned on, the startup transistor (NM4) pulls down on the V_X4 node, which turns on the PMOS load transistors (M1, M4), taking the BGR from the zero-current state into the active operating region. During this stage, the biasing voltage VNM4 for the NM4 is very high which guarantees its conduction. The startup circuit must turn off once BGR settles so that unnecessary power dissipation does not take place when NM5 is turned on by a high potential at V_X3, pulling down the N4 node, consequently turning NM4 off and ensuring that the startup circuit is disabled after initialization. After stabilization of the BGR core, the startup circuit acts as a normal turn-off circuit that prevents any unnecessary power from being consumed, as is seen from the startup transistor (I_NM4) reverting to zero at 120 µs.

Figure 5 presents the output occurrence graphs of CM-BGR and Cascaded CM-BGR under a supply sweep at 4 V. The results indicate that the Cascaded CM-BGR is able to maintain its target output voltage of 1.05 V, thus demonstrating its stability against supply changes. On the other hand, the CM-BGR demonstrates large deviations in its output voltage, tending towards higher supply levels in the samples. Such deviations indicate that the CM-BGR is more sensitive to supply changes, thus less stable.

BGR circuit design using operational amplifier

Operational amplifiers are used in applications where there is high gain and high speed. A differential input and differential output multi-stage configuration makes the circuit highly stable. With this configuration, differential signals are amplified and common-mode signals and noise are rejected simultaneously¹⁸. Differential inputs, V+ and V −, are connected to transistors M9 and M10 as shown in Fig. 6. A differential voltage can be translated into a differential current by these transistors, which form a differential pair. Transistors M1, M2, M3, and M4 also form the current mirror circuit, which provides the active load impedance of the differential pair.

The first stage consists of the differential pair (M5, M6) and the current mirror load (M1, M2). The gain of this stage is

A2 is the gain of the second stage (Common Source Amplifier)

Figure 7a, b illustrates how the phase response of the circuit changes when frequency is altered. Phase margin, or the phase shift from − 180°, is highly significant in establishing the stability of the amplifier.

At differential gain, differential gain is the difference between the Vout gain and the gain of V+, V−, with intermediate nodes (Vy1, Vz1) considered. Ripples and peaks at high frequencies indicate parasitic effects or insufficient compensation. A sudden voltage gain vs. frequency spike in Fig. 7c might indicate resonances or noise coupling within the circuit. A plot of CMRR (Fig. 7d) illustrates the difference between the differential signal and the interference resulting from common-mode signals. The higher the CMRR, the higher the rejection by a differential amplifier of common-mode signals and noise.

A BGR circuit generates stable voltage that is independent of temperature, supply voltage, and process variations. Q1, Q2, Q3, Q4, Q5 and Q6 generates the CTAT voltages (VBE1, VBE2). R1 determines the current I1, which is proportional to the voltage difference VBE1–VBE2. R2 scales the PTAT current to generate the required voltage at the output. The operational amplifier enforces a virtual short condition, ensuring that the voltages at its inputs are equal¹⁹.

Operational Amplifier-based Bandgap Reference (BGR) circuit functions based on the production of a process-insensitive and temperature-stable reference voltage^7,20,21. The operational principle of this circuit is the integration of two voltage terms with opposite temperature coefficients: the base-emitter voltage (VBE) of a bipolar junction transistor (BJT), with a negative temperature coefficient, and thermal voltage (Vt)⁷. The nomenclature is derived from the resistor network that exhibits a positive temperature coefficient. The operational amplifier provides for proper biasing by equating the voltages at its input terminals (V_BE1, V_X), thus ensuring the desired current flow through the BJT network as shown in the Fig. 8a. The current is copied across multiple transistors (M0, M1, M2) to provide a voltage proportional to absolute temperature (PTAT), which is then added to the complementary-to-absolute-temperature (CTAT) results, producing an effectively temperature-insensitive output voltage. The resistive ratio determines the PTAT voltage value, allowing precise reference voltage adjustment, typically to 1.2 V. MOSFET-based current sources offer a stable bias condition, with minimal supply voltage sensitivity. Figure 8b shows the relation between R_BGR and slope of V_BGROUT3 for the range of temperature − 40 °C to 125 °C. R_BGR is adjusted to 139KΩ bring PTAT strength which equals to CTAT. The simulation results demonstrate the range of R_BGR for which slope of V_BGROUT3 is constant²².

Sub-BGR circuit design using operational amplifier

The circuit shown in Fig. 9a is a sub-BGR, which produces constant reference voltage through current summing technique^5,9. The sub-BGR is achieved using bipolar junction transistors (BJTs) (Q1–Q5) to produce base-emitter voltages (V_BE) with negative temperature coefficient (CTAT). The R1 resistor is used to produce a current with positive temperature coefficient, since the differential CTAT voltage (V_BE1–V_BE2) produces a voltage drop across it, which essentially produces a proportional-to-absolute-temperature (PTAT) current. Since V_X is a CTAT voltage, the voltage drops across R2 produces a CTAT current. The sum of PTAT and CTAT currents flow through M1 to make the resulting overall current constant²³. M2 mirrors the constant current to resistor R0, where the combined CTAT and PTAT components produce a stable reference voltage at V_BGROUTC1. A PMOS current mirror (M1) supplies stable bias currents to facilitate proper circuit operation. An operational amplifier keeps equal voltages (V_BE1 and V_X) at its inputs to facilitate proper generation of the PTAT current. The PTAT current, produced by the difference between the base-emitter voltages (V_BE1 and V_BE2) of the BJTs and scaled by resistor R1, is summed up with the CTAT current at the output node to facilitate temperature-compensated reference current²⁴. This current, when passed through RBGR, produces a stable output voltage (V_BGROUTC1).

Figure 9b plots the output voltage (V_BGROUTC1) variation with temperature for different R_PTAT values, which reflects the effect of R_PTAT on temperature stability and the operation of the bandgap reference. The ideal bandgap reference should have a stable output voltage irrespective of the temperature change, with proper temperature compensation¹⁹. When R_PTAT is scaled PTAT behavior is dominated and slope of output voltage (V_BGROUTC1) is also changes, thus R_PTAT is determined based on the V_BGROUTC1 slope.