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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.

A century ago, the County Limerick village of Kilteely had seven pubs but one by one they shut. This year, it braced to lose the last.

The economic and social trends that have shuttered family-run pubs across Ireland appear remorseless, leaving many communities with nowhere to meet, have a drink and share stories.

But this week Kilteely bucked the trend. The doomed bar reopened after 26 villagers clubbed together to buy it. “We felt we were going to be annexed into other communities if we didn’t have a place to meet and call our own,” said Liam Carroll. “So here we are, we’re publicans.”

The new owners pooled their savings and formed a syndicate to buy the pub, which otherwise faced probable demolition and conversion into accommodation.

The eclectic group – which includes a barrister, a solicitor, a pharmacist, a clinical psychologist, a carpenter, an accountant, a teacher, a signmaker, builders, farmers and electricians – bought the bar and licence for €300,000 (£260,000) and used its varied skills to reestablish and refurbish the business.

Previously Ahern’s, the pub is now called the Street Bar, a reference to the local expression “heading up the street”, a euphemism for heading out for a pint. (Some syndicate members wanted to call it the Ambush, after a famous 1921 attack during the British-Irish war that killed 11 soldiers and police, but that was vetoed.)

It has new wiring, a cool room for beer, Sky Sports and, tucked between wine and whiskey, a sign: “Welcome to the Street Bar. A community working together in Kilteely.” Another sign lists syndicate members.

“We hope other communities will see that it can be done,” said Carroll, the barrister. “All these closures – it doesn’t have to happen.”

Since 2005, Ireland has lost a quarter of its pubs: more than 2,100, averaging 112 a year, according to a study commissioned by the Drinks Industry Group of Ireland. The phenomenon is highest in rural areas. At county level, Limerick, in the south-west, recorded the highest decrease of 37.2%.

Multiple reasons are cited: the cost of living, high taxes on alcohol, drink-driving laws, young people drinking less, preferences to drink at home, the Covid pandemic and shrinking profit margins. A similar trend has closed 15,000 pubs in England, Wales and Scotland since 2000, according to the British Beer and Pub Association.

Having already lost post offices, shops and other pubs, the closure of Ahern’s – which had been kept afloat by Noreen Ahern, who is near retirement age, working an estimated 90 hours a week – would have left Kilteely’s main street empty and abandoned, save for a recycling business.

Rather than mourn, some residents proposed a rescue based on an example from the County Waterford village of Rathgormack: in 2021, 19 local people formed a syndicate to buy and run the last pub, which was due to close permanently.

A group of 20 Kilteely residents each contributed €15,000 to meet the €300,000 price and turn the pub into a private limited company with a social enterprise ethos. “We made clear to all who invested that they should expect not to see a return of their money,” said Carroll.

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The group divided tasks such as paperwork, accounts, electrics and carpentry according to skillset, said Gerry O’Dea, 54, a farmer and financial adviser. “Everybody brought something to the table.”

Heeding advice from the Rathgormack syndicate, the Kilteely group separated ownership and management. “You couldn’t run a pub where you have 20 people with different opinions about the price of drinks,” said Carroll.

The shareholders appointed a five-member board that in turn hired a manager who, unlike them, had experience running a pub. “You hire the best people and get out of their way,” said Eoin English, 50, an engineer. The pub would remain a gathering point, he said. “This is where people have birthday parties or post-funeral receptions.”

Daniel Kreith, 29, a solicitor and syndicate member originally from Galway, said his home village had lost nine of its 13 pubs. Kilteely showed that decline and oblivion was not inevitable, he said: “Some of them could have been saved.”

The model appears to be spreading – County Kerry’s first community-owned pub is due to open soon.

Bosco Ryan, 56, another Kilteely syndicate member, said stakeholders and their friends and families formed a network that could help sustain the Street. “We all have a responsibility to support it.”