The Dog at the Corner Shop - by ChatGPT out of Alexander McCall-Smith

I just finished reading The Perfect Passion Company by Alexander McCall-Smith. He's best known for his Mma Ramotswe series, The No 1 Ladies Detective Agency, but he has written lots of others too. This one is (at least for now) a stand-alone. He writes with a very characteristic style, which I would describe as philosophical tenderness. Nothing awful ever happens, and even mildly bad things aren't allowed to go too far. All described kindly, accompanied by his own vaguely philosophical reflections on life and humanity.

When I finished it, I asked ChatGPT to "write a short story about a man and a stray dog in the style of McCall-Smith". I was amazed by what it produced, which absolutely echoes his style both linguistically and in feeling.

I also asked it to do the same in several other styles. Thomas Hardy was quite convincing - you can try it for yourself.

I know the theory of how LLMs work, but I still can't figure out how it can do stuff like this.

The Dog at the Corner Shop

There are many curious things that happen in a city, even in the quieter corners where streets are lined with linden trees and elderly ladies take the air while discussing the price of courgettes. One such corner lay at the meeting of Rue de la Forêt and the smaller, humbler Passage des Perles. It was here that Mr. Andrew Bell, a mild-mannered man of unassuming habits, found a dog.

It was a cool morning in early spring. The baker next door had just opened, and the warm perfume of risen dough drifted through the doorway like a warm, well-mannered guest. Andrew had stopped to purchase his usual country loaf. He believed, quite properly, that a person should have a relationship with his baker—mutual, respectful, and ideally punctuated by crunchy crusts.

As he stepped outside with his loaf, he saw the dog sitting—politely, it must be said—beside a stack of bottled water at the door of the corner shop. It was a wiry creature with caramel fur and alert amber eyes; the sort of dog who would undoubtedly know the price of courgettes, if such knowledge were ever required of him. He regarded Andrew with a patient, philosophical expression, as if he were accustomed to considering deep matters but had chosen, that morning, not to trouble himself.

Andrew paused. He did not usually speak to animals, having grown up in a household where pets were considered enthusiastic but unnecessary, like unnecessary commas. But the dog looked at him as though introductions were in order.

“Well,” Andrew said, “good morning.”

The dog wagged his tail once, a measured gesture indicating that the greeting had been received, processed, and approved.

“Are you waiting for someone?” Andrew asked.

The dog sighed—an elegant, dignified sigh—and stood. He walked directly to Andrew and sat at his shoe. It was a clear request: We may proceed now.

Inside the corner shop, Monsieur Lavigne, proprietor and commentator on all matters of consequence in the neighbourhood, adjusted his glasses.

“This dog has been here since dawn,” he announced. “He came with no one, and he has eaten nothing. Just sits there, comme ça.”

“He seems friendly,” Andrew said.

“Friendly, yes,” Lavigne agreed. “But unaccompanied. This is often how great adventures begin.”

Andrew contemplated this. Adventures were not generally part of his plans. His calendar contained items like the dentist and replace the vacuum bag. Dogs were not listed anywhere.

Still, the animal had chosen him.

Andrew took the dog home, where he gave him water in a salad bowl. The dog drank politely, not spilling a drop. He ate small amounts of cheese with gratitude, but not greed, as though he were mindful of cholesterol. Andrew found this admirable.

He telephoned the local shelter. No one had reported such a dog. He walked to the police station, where the officer on duty, who was not busy, asked if the dog had any discernible talents. Andrew didn’t know.

“He seems thoughtful,” he offered.

The officer wrote this down carefully.

Days passed. The dog—whom Andrew had begun to call Hugo, because a dog should have a name—made himself quietly indispensable. He rode the lift without complaint. He sat companionably by Andrew’s feet while he read. He nudged Andrew at exactly the right moment each morning, just before the alarm, making alarm clocks quite redundant.

One Saturday, as they walked along the river, they encountered a woman in a blue coat examining a map. She looked up and gasped.

“Hector!”

Hugo—Hector—bounded to her, tail sweeping the air with such delight that even the river seemed pleased. The woman embraced him. She looked at Andrew with shining eyes.

“He ran away during the storm. I thought I’d lost him forever.”

There was joy, of course—joy for the woman and joy for Hector, whose tail proclaimed reunion. But there was also a small, unexpected ache in Andrew’s chest.

“You’ve taken good care of him,” she said. “Thank you.”

Hector barked once, as if agreeing that Andrew had done well.

The woman smiled. “Would you—would you like to visit him sometime? He makes friends, but… he rarely chooses a person so completely.”

Andrew nodded. “I’d like that very much.”

Weeks passed. Andrew visited Hector every Sunday. They walked in the park and sat on benches, contemplating ducks and the secular miracles of sandwiches. Andrew looked forward to these visits in a quiet, steady way.

Life, he reflected, was sometimes like that. We are given companions for a short while—just long enough to remind us that friendship is everywhere, even on street corners where no one expects it, and even in the shape of a small dog with amber eyes.

And so it was that Andrew’s world grew just a little larger—and his baker, who knew these things instinctively, began including small leftover pastries in a paper bag, “for your philosophical friend.”

Because even in the simplest lives, there is room for a small miracle or two—and often, they arrive with four paws and an unhurried tail.

To Penzance, Finally

Just arrived in Penzance - a Hitachi 802

The Dream

I’ve been a regular user of London’s Paddington station for half a century now, first during the time when I lived in and around Reading, for which it is the London terminus. Later it became the London end of the Heathrow Express, which has taken me there regularly ever since.

At railway stations as well as airports I can’t resist looking at the destination display, of all the places I could be going to. And the one that has struck me every single time I visit Paddington is Penzance. It’s the very last town in England at the south-western tip of the Cornish peninsula, just 9 miles from the end of the world at Land’s End - next stop, America. For over a hundred years it is probably best known as the setting of the Gilbert and Sullivan operetta The Pirates of Penzance, though probably chosen by them more for alliteration than anything else.

Lately I have been telling myself that I should stop dreaming and just hop on a train and go there. And finally, taking advantage of a Thursday meeting near London, we did just that. It seems a shame to go all that way and not explore the countryside, so we left on Friday and returned on Sunday afternoon.

The Journey

British trains don’t have a great reputation these days, but our train journey from London was superb. The trains are nearly-new Hitachi 802 class, and the first-class seats are extremely comfortable. The only drawback is the club-style layout, meaning you potentially spend five hours playing footsie with a total stranger. But luckily we found some unassigned single airliner-style seating, for which we abandoned our reserved seats to sit in comfort for the rest of the journey.

We were very pleasantly surprised by the service on the train, as it whizzed through the pretty Berkshire countryside at 120 mph. It left at 10am, meaning the five hour journey spanned lunchtime, but we were served an endless stream of coffee, tea and best of all, Walkers ginger biscuits, as well as a decent sandwich for lunch.

A highlight of the journey is the line westward from Exeter to Newton Abbot, which includes the famous sea-wall stretch at Dawlish. The railway was built right next to the sea, with only a low wall protecting it. It is periodically flooded, and every now and then washed away altogether, a result of the engineering compromise of building the line along the coast where there were plenty of towns and villages to serve. The London and South Western Railway took the inland route, easier to build but serving a much smaller population. Today only the coastal Great Western line survives. It’s a spectacular sight, with only a few hardy souls strolling on the beach between the train and the open water.

The next spectacular sight comes just after the stop at Plymouth. Here the line crosses the River Tamar on Brunel’s magnificent 1859 Royal Albert Bridge, with great views over the mudflats of the estuary. And then, after three hours, we were in Cornwall. The train had been slowing down gradually throughout the journey, and from here it trundles through the Cornish countryside at a sedate 60 mph. Up to Plymouth it made just four stops, but now it turns into almost an all-stations service, abandoning all pretence at being an express. That makes sense, because there are no large towns in Cornwall. The two hours it takes to cover the remaining 100 miles to Penzance are anything but boring. There is a constant panorama of deep valleys and rolling countryside populated by cows and sheep, and the occasional derelict tin mine with its pump building and chimney.

Approaching Penzance the sea comes into view again, before the train pulls into its final stop. I’d seen pictures of Penzance station, generally including one of the original GWR’s magnificent King or Castle class steam engines. The station is nestled against the sea, a car park replacing what was once the goods yard. Main-line terminal stations are fairly rare in Britain’s provinces, and Penzance must surely be the ultimate terminus - beyond, there is nothing, and somehow the station manages to evoke that.

Our arrival coincided with the departure of one of the few High Speed Trains (HST) remaining in service. In their day these were fantastic trains, the first to exceed 100 mph in regular service - they were branded as HS125, for their speed. Watching one depart was always a pleasure, the rear engine roaring past at a respectable speed as the train accelerated out of the station.

One of the last HST sets in service, about
to depart for Plymouth

It’s amazing they are still in service - they replaced the Western Region diesel-hydraulics in about 1976 and so have been in service now for 50 years. I well remember a ride to Edinburgh in about 1980, where they had recently replaced the equally impressive Deltics. Sadly they will all be withdrawn later this year, and they don’t really lend themselves to preservation. This one was ignominously on an all-stations service to Plymouth, where it would never reach even half of its capable speed.

Arrival

Penzance is too small to host any of the usual car rental companies. Luckily I had found a local company which rented us an elderly Renault Clio at a high price - but at least we had a car. The choice of hotels is limited. There are a couple of soulless modern hotels on the outskirts, and plenty of AirBnB type places. The only actual hotel in the town itself is the Queens Hotel, which overlooks the promenade and the beach.

It was built in 1862, with the arrival of the railway from London, and seems little changed since - the best word for it is “quaint”. It has a frontage of 100 metres or so, and must have about 70 rooms. Our room was pleasant enough, big and with a great view over the sea. Apart from an occasional repaint I suspect it hasn’t changed since the 1950s - one giveaway is that there is no shaver socket in the bathroom, which was tiled in a stylishly dated light turquoise.

Once installed, we headed inevitably for Lands End. We passed through the picture-postcard village of Mousehole, pronounced ‘mowzel’, and then along a series of country lanes, often too narrow for two cars to pass. Oddly the signposted distance to Lands End remained at 9 miles for about half the journey.

The place itself is an odd blend of Disneyland and desolation. There is a resort with all kinds of not-so-attractive attractions (and exorbitantly overpriced parking), but on a grey October day almost nothing was open. We walked down to the viewpoint, where a forlorn poster offered photographs in front of a sign showing distances to various faraway places in the world - though there was no photographer amongst the handful of people huddled against the wind. A walk around the hotel revealed a refreshment room, its windows fogged up and one sad-looking couple visible inside. We weren’t tempted. Oddly it reminds me of the small coastal towns in Japan we’ve visited, where even outdoors you can almost smell the mould and decay.

Back at the hotel, Isabelle went for a walk and discovered the Morrab Gardens, a beautiful collection planted in the late 19th century, similar to the English gardens to be found along the Cote d’Azur. Then it was time to think about dinner. Our first attempt was a busy pub round the corner from the hotel, but surprisingly they didn’t sell food. We took the car and drove along the promenade to another place suggested on the web. That turned out to be surreal.

As we entered, at just 7.30 on a Friday evening, the staff looked at us in a mixture of surprise and horror. After a brief huddle, they declared that the kitchen was already closed! In California we were used to the “early to bed” philosophy - by 8pm most restaurants are putting the chairs on the tables, and by 9 the streets are deserted. But we weren’t expecting that in Britain. Luckily, another no-food pub suggested a little place hidden away in an alley, the Barbican Bistro. And there, we had really lucked out. We had really excellent fish, sole and hake, imaginatively prepared and followed by an equally excellent creme brulée.

But now there was absolutely nothing to do except to retire to bed, which we did at the extraordinarily early time, for us, of 10.30. There must be something in the Cornish air though, because we didn’t wake up until 8.30, after ten hours of sleep.

Our hotel rate included breakfast, which was served in a vast, empty room, with just a couple of rows of tables defensively hugging the windows. The menu looked appetising enough, but was let down by the implementation. I asked for some honey to accompany my porridge. They offered me maple syrup instead, which I gratefully accepted, but I had poured a generous amount of the offered product into my breakfast before I realised that its origins owed a lot more to the chemical industry than to maple trees. It had a peculiar odour and taste, a mixture of soy sauce and burned meat, that rendered the remainder of my porridge inedible.

An attempt to buy a map and guidebook led us to the town centre, the oddly named Market Jew Street. The town is in the throes of a massive rework of its road system, which has turned what would normally be the through roads across the town into a series of dead-ends. The main street is totally inaccessible even to delivery vehicles, and apparently all goods have to be manhandled from remote back streets on trolleys. You really have to ask yourself what goes through the mind of people who come up with schemes like this.

We found a nice bookshop (The Edge of the World Bookshop) but the main street is a bit of a sorry sight. About a quarter of the shops are boarded up, and several of the others didn’t look very open. The town as a whole has a tired, semi-derelict feel to it. Maybe it’s different when it’s packed wth summer crowds.

Winery

Rondo grapes at the Polgoon winery

It’s always interesting to visit a winery, to see how they adapt to the local climate and terroir. Penzance has its very own, Polgoon, on the edge of the town though rendered almost inaccessible by another massive set of roadworks. It takes real talent to shut down the town and the only available bypass simultaneously.

Polgoon introduced to several grape varieties we didn’t know before: Bacchus, Rondo and Seyval Blanc. We were impressed that they manage to convince any grapes to grow in the Cornish climate, even though none of them were really to our taste. Bacchus produces a white wine with an almost meaty taste. Rondo is impressive more for its foliage, with huge russet-red leaves.

The very pleasant lady at the winery recommended several restaurants, and for lunch we went to the Mackerel Sky Seafood Bar in nearby Newlyn. They served a kind of fishy tapas selection, which was delicious: scallops, crab nachos and battered halibut, accompanied by cider from Polgoon.

The Communications Museum

In the afternoon we resisted the temptations of St Ives, apparently a hotbed of fancy art galleries and general tourist attractions, and headed for the Communications Museum at Porthcurno. Cornwall is the logical jumping-off point for cables across the Atlantic or south towards Africa. The site of the very first cable - towards India, not America - was chosen because of its remoteness, and the impossibility of bringing a boat close to the shore, with the risk of damage to the cable.

Connector, 1930s style, at the
Communications Museum

In the beginning, forwarding a message from one cable to another - a job now done billions of times per second by network switches and routers - required manual interpretation of the incoming Morse code, and manual retransmission. It was very labour intensive, requiring an army of meticulously trained telegraph operators. Logically enough, the school established for this purpose was at Porthcurno. It lasted for nearly a century, finally closing in 1970. Life must have been absolutely monastic, especially during the half century before cars existed.

Many of Britain’s undersea cables terminated there. During the two World Wars it was of vital importance, so much so that during the Second War, its functions were removed into tunnels carved deep into the granite. The exhibition includes various pieces of contemporary equipment and the story of the cables, the school and the people. It beats parading round overpriced touristy art galleries any day!

After winding our way back along the often one-track roads, we had dinner that evening at a restaurant called Cork and Fork, which was also very good.

I was surprised how few Cornish accents I heard. Nearly everyone we dealt with could have come from within a 50-mile radius of London. A few older people did have the local accent, though it seems very mild compared to Geordie (from around Newcastle) or (heaven forbid) Glasgow.

Departure

St Michael's Mount with Ferry

The next day our train was at 1215, which left us time to do something in the morning. One of the famous sites is St Michael’s Mount, but oddly it is closed on Saturdays so we hadn’t been able to visit it the previous day. The proper tourist thing to do is to walk out to it along the causeway, which is only accessible for a few hours at low tide, but the tides weren’t cooperating that day. At other times, little boats run almost continuously, taking just a few minutes to cover the couple of hundred metres out to the island. We just about had time to take the boat out, walk around the harbour and the museum, and get the boat back, before returning via the nightmare mess of closed roads to the station. It was well worth it, and just maybe one day we will return and hike up to the castle at the top of the mount, and visit its famous garden too.

The Great Western train back was just as enjoyable as the outward journey, though it would have been even better if there had been a King or a Castle on the front of the train, one of the Great Western’s famous 1920s steam engines. Still, I did manage to blag a visit to the cab at Paddington, just as I did when I was tiny and my Dad would hoist me onto the footplate of a newly-arrived Britannia Pacific at Liverpool Street. It seemed vast, with the gaping maw of the red-hot firebox in pride of place. The Class 802 was a superb display of modern railway technology, but not as terrifyingly impressive.

The "Footplate" of our Hitachi 802
just arrived at Paddington

Tubes 201 - How Vacuum Tubes Really Work, Part 9: Tube Designators

← Previous: Other Topics

Each different type of tube received an identifier, or designator, for example 12AX7, EABC80 or 300B. Some kind of identification was obviously essential, as for any electronic part, just so that users can order the parts they need. The tube identifiers were generally independent of any particular manufacturer, so the corresponding tube could frequently be obtained from different sources.

There were two main systems in use: Philips in Europe, giving codes like ECC83; and RETMA in the US, giving designators like 6SN7.

Philips Coding

Despite the name, this coding was used by nearly all European manufacturers, with Mazda as the principal exception. It was invented and maintained by Philips and Mullard.

The first letter specifies the filament requirements. By far the most common letter is E, meaning 6.3V. Televisions and older AC/DC radios didn't have a fixed 6.3V filament supply. Instead, they wired all the heaters in series across the AC power. That meant they had to use the same current, generally 300 mA for televisions and 100 mA for radios, rather than the same voltage. Philips encoded fixed-current filaments specially. Commonly-used codes were as follows:

	D	1.5V for battery operated radios
	E	6.3V
	G	5V for B+ rectifiers
	O	cold-acthode tubes, e.g. voltage regulators
	P	300 mA series connected, for televisions. If that happened to result in a 6.3V filament, like the ECC8x twin-triodes, E was used rather than P
	U	100 mA series connected, for AC/DC radios

There were many other assigned codes (for example, for 2V battery operated radios), but by 1950 they were all obsolete.

The second and subsequent letters described the elements of the tube, as follows:

	A	signal diode
	B	twin signal diode with shared cathode
	C	small signal triode
	D	power triode (rarely used)
	F	pentode
	H	hexode frequency changer
	K	heptode or octode frequency changer
	L	beam tetrode
	M	magic eye
	Q	nonode (only one, the EQ80)
	Y	EHT rectifier
	Z	B+ rectifier

These could be combined as required. So 'CC' was a twin triode, 'CF" was a triode plus pentode, and 'ABC' was a triode combined with a single diode and a dual diode (used in FM demodulators).

The first digit described the base:

	None	Philips side-contact
	1	meant "look at the second digit", e.g. EF180
	3	octal
	4	8-pin Rimlock
	5	miscellaneuous - anything not covered elsewhere
	7	Loctal (little used since Loctal tubes were rarely used in Europe)
	8	B9A 9-pin
	9	B7G 7-pin

Meanings were assigned to other values but were rarely used.

Remaining digits were just used to identify specific types, and had no meaning.

Some examples:

• ECC83: 6.3V twin triode with B9A base
• UCH81: 100 mA triode-hexode frequency changer with B9A base
• EC90: 6.3V single triode with B7G base
• PL500: 300 mA power pentode with large 9-pin base
• ECC33: 6.3V twin triode with Octal base (near-equivalent to the 6SN7)
• GZ40: 5V full-wave rectifier with 8-pin Rimlock base

The digits could immediately follow the first letter, with the element descriptor coming afterwards, e.g. E182CC. This indicated a "special quality" tube, made for example to have an extended life for use in computers.

US Coding (RETMA)

The US codes give less information about the tube than the Philips code.

The first number is the filament voltage. '6' means 6.3V. There is one exception: '7' normally means a 6.3V heater, but with a Loctal 8-pin base - except for a tiny number of tubes that really did have 7V heaters (like the 7DJ8/PCC88, a 300 mA version of the 6DJ8/ECC88).

The letters had no meaning. They were assigned serially, in general, as required.

The last digit is the number of distinct "elements" in the tube. This is a count of the electrodes, with the filament counting as a single element. So a 6SN7 has a 6.3V filament, two triodes of three elements each, and the filament, giving a total of 7.

Any letters after that describe the specific envelope. 

• Originally the absence of a letter meant a metal outer envelope, like the 6CA7, but for miniature tubes it meant a conventional tubular glass envelope, e.g. 12AX7
• G' meant a coke-bottle style envelope, like the 6AS7G.
• 'GT' meant a squat, tubular glass envelope, like the 6SN7GT
• 'A", 'B' or 'C' meant improved versions, so a 6SN7GTA was an improved version of the 6SN7.

There was no special treatment for constant-current tubes, which were designated by whatever voltage happened to correspond to the required current. For example, the 27BG5 was the equivalent of the PL500, a 300 mA power pentode that happened to require 27V.

Other Codings

• Special tubes carried a 4-digit number in order of their introduction, for example the 5692 which was a special quality version of the 6SN7
• Western Electric had their own coding, generally a 3-digit sequential number possibly followed by a letter, e.g. 300B, 417A
• The UK company Mazda used the Marconi-Osram coding, e.g. the KT88 beam tetrode
• Very old tubes carried whatever number their original manufacturer gave them, e.g. 76

← Previous: Other Topics

Tubes 201 - How Vacuum Tubes Really Work, Part 8: Other Topics

← Previous: Noise

Next: Tube Designators→

Secondary Emission

When an energetic, fast-moving electron hits a metal surface, the impact dislodges some of the other electrons and causes them to be emitted. An electron arriving at a 250V plate has an energy of 250eV, whereas the metal's work function means that only around 4eV is required for an electron to be emitted. This phenomenon is called secondary emission, and occurs each and every time an energetic electron arrives. Under normal conditions, the plate is the most positive thing around, and these secondary electrons are simply attracted back to the plate where, having only a little energy, they are re-absorbed without provoking any further emission. This is benign and has no effect on the electrical operation of the tube, and is indeed unmeasurable

Secondary emission only becomes a problem when the emitting surface is not the most positive thing nearby. In this case the emitted electrons are captured by the electric field and form a secondary current between the two electrodes. For example, if the grid of a triode is made positive rather than negative, and more positive than the plate, so that electrons flow directly to it, then the secondary electrons will be attracted to the grid, causing a flow of current away from the plate

Secondary emission - or more accurately, secondary current flow - is almost never a good thing. It occurs unavoidably in the tetrode (as described below) and is the principal reason why tetrodes have been replaced by pentodes. It was exploited in photomultiplier tubes, as a way to multiply a very feeble initial current. There was also a tube in the late 1930s, the Philips EFP60, which used secondary emission from a target electrode as a way to increase the Gm, but it proved difficult to build predictably and was not successful. The problem is that although secondary emission can be measured for a particular metal, and in principle allowed for, in practice it is heavily affected by surface contaminants and the like. It cannot therefore be used as a reliable element of a tube's operation

Vacuum

In theory, the inside of a tube's envelope is a vacuum. In practice, a perfect vacuum is unachievable, and a certain level of residual gas has to be accepted. The pumps that are used to evacuate tubes can typically get down to about 10^-7 mm of mercury, or about 10^-10 of atmospheric pressure. However once the tube is sealed, gas can still get into the space inside it. First, the glass-to-metal seals around the pins or lead-out wires are not perfect, and allow small amounts of air to pass. Secondly, a certain amount of gas is adsorbed at the surface of the metals, mica and glass inside the tube. Under the high vacuum, this gas is slowly released, particularly if the surface is raised to a high temperature. This is the main reason why allowing the plate of a tube to overheat is bad. It results in a sudden release of gas, faster than the getter can absorb it, which interferes with the tubes operation and can rapidly result in destruction of the cathode

An essential part of the structure of all tubes is the getter, the silvery coating to be seen somewhere on the glass envelope. It is generally made of barium, which when hot reacts with gases, taking them out of circulation as soon as they appear. As the tube ages, the getter is gradually used up. Anything resulting in a serious gas leak will exhaust the getter quickly, and this can easily be seen because its appearance changes from silvery to white. In manufacture, the getter is placed inside a special container, often a small cup which can be seen attached to the internal structure close to the getter location on the envelope. Once the tube has been exhausted by a pump, and sealed, the getter is fired either by passing an electric current or using an induction heater. Thus the film is deposited on the envelope

If the vacuum is not perfect, and we have seen that it never is, then some gas molecules remain inside the tube. When an energetic electron hits such a molecule, it generally knocks one or more of the electrons out of it, resulting in a positively charged ion. This is then attracted in the opposite direction from the electrons, i.e. towards the grid and the cathode. The majority of these hit the cathode. Here their energy is able to dislodge the surface atoms, particularly in oxide cathodes, which is called cathode stripping. The gradual erosion of the cathode surface is one of the principal factors limiting the life of small tubes. This is why tubes should ideally not have plate voltage applied until they are warm, since in this way the getter has a chance to deal with gas molecules which have appeared since the tube was last operated

The chances of an individual electron colliding with a gas molecule are very small. In a new tube an electron could travel around 10 kilometers on average, before having such a collision. However, because of the large number of electrons involved in carrying the current, the number of such ionisation events is large around one billion per second for a small tube in typical conditions, with a good vacuum (10^-7 mm Hg).

Tube testers estimate the vacuum in the tube by measuring the negative grid current under determined operating conditions. The higher the current, the more gas that is present. In a new tube with near-perfect vacuum, this current is much less than 1 μA, but if a tube starts to lose vacuum it becomes measurable.

Interelectrode Capacitance

Any closely-spaced conductors have a capacitance between them, and the electrodes of a tube are no exception. In a triode, the capacitance from the grid to the plate and the cathode respectively could in principle be worked out from the tube dimensions. Typical values are a few pF for each of them, for small-signal tubes. Large-signal tubes have higher values, simply because of the larger electrode areas.

There is also capacitance between the lead-out wires. This is very small, but it can be enough to cause RF oscillation if this is not damped by resistors close to the tube base.

There is also a capacitance between the plate and the cathode, but this is reduced by a factor equal to µ from what the normal capacitance formulae would give. Typical practical values are 0.5-1pF, which is largely due to the lead-out capacitance.

Finally, the very close spacing between the cathode and the heater packed inside it also results in capacitive coupling, typically around 1pF. This allows noise and RFI, in particular, to couple from the heater supply into the signal, and vice versa.

The most common amplifier circuit is the common cathode, but the interelectrode capacitance causes a particular problem in this configuration at higher frequencies. As the grid voltage rises, the plate current increases and hence the plate voltage falls by an amount equal to the amplification of the circuit. But this falling voltage is capacitively coupled back into the grid, leading to the Miller Effect in which the effective value of the grid-plate capacitance, as seen by the driving circuit, is multiplied by the gain of the circuit.

This is a big problem for RF, but it can be significant for audio too, depending on the circuit design. Whereas a value of say 4pF would have little effect, at audio frequencies, the Miller Effect results in a value of several hundred pF.

The cascode input stage design, with two tubes effectively in series, nearly eliminates Miller Effect, at the cost of an extra tube element. At very high frequencies, for example in a UHF tuner, a grounded grid circuit must be used.

Grid Current

Since the grid has no physical connection to anything (as the circuit symbol shows), it is natural to think of it as being electrically isolated. In fact, this is not the case, because of the flow of electrons and ions inside the tube

Current flow to and from the grid arises for two reasons. The most obvious is when the grid is positive, which causes it to attract electrons. Less obviously, when the grid is negative, it attracts positive ions resulting from collisions between electrons and gas molecules. These cause the grid to become less negative. It is because of this effect that the grid must never be left truly floating but must always be connected through a resistance, typically for a small tube not more than 1MΩ. Without this, the voltage of the grid will gradually creep up, reducing negative bias and increasing current through the tube and leading to a runaway which, at worst, will destroy it through overheating. As mentioned above, tube testers measure negative grid current as a proxy for gassiness.

At the right voltage, these two currents cancel out. This normally occurs at around 0.5V (depending slightly on plate voltage), which is slightly positive relative to the virtual cathode. If the grid is simply left disconnected, it will float at this voltage, and the plate current will correspond to this level of bias. This is the basis for a so-called leaky-grid detector, since operation in this region is very non-linear.

Positive grid current is deliberately used in some cases, for example in high-µ transmitting tubes. When it occurs, Child's Law gives, not the plate current, but the sum of the plate and grid current. This is because total current is controlled by the field in the immediate vicinity of the cathode, which is due to the combination of the two other electrodes. To calculate the actual plate current (and hence also grid current), it is necessary to know how much of the electron stream flows to each of the two electrodes. This is given from the following formula:

$\frac{I_p}{I_g}=\delta \sqrt{\frac{V_p}{V_g}}$

where:

$\delta$ = current division factor

The current division factor $\delta$ is slightly greater than the shielding ratio of the grid. If grid current curves are available for a tube, it is easy to determine its value from them.

Unfortunately this tidy formula only gives the value for the primary current. Once the grid is more positive than the plate, secondary emission will start to occur, resulting in a secondary current flow from the plate to the grid and reducing the effective grid current. This is, for all practical purposes, unpredictable. Depending on the tube, the secondary current may even exceed the primary current, typically at around 30-50V. This results in a second stable voltage for a disconnected grid at the point where the primary and secondary currents exactly balance

Positive grid current results in heating of the grid, for the same reason that the plate gets hot (i.e. due to the kinetic energy of the arriving electrons). Small tubes are not generally designed for this, but power tubes and especially tubes designed for positive grid operation have substantial dissipators attached to the grid structure.

Overheating of the grid is bad for two reasons. Firstly, since it is not designed to run at a high temperature, it does not have any way to retain its tension as the metal expands. This results in changing geometry and in the worst case melting or a short to the cathode, which is instant death. Secondly, the grid is generally contaminated by oxide from the cathode, and if it gets hot then it will start to emit electrons like the cathode, resulting in a substantial secondary current

Close Electrode Spacing

Because $G_m$ increases inversely with the square of the grid-cathode distance, tube designers have always been under pressure to reduce this distance. However, if it falls below the grid pitch, the design assumptions of the triode start not to apply. The field is no longer uniform at the cathode, but rather varies, becoming less negative between the grid wires. In fact, if the separation falls below 0.6 of the pitch, the $G_m$ starts to fall again. As a result, the evolution of vacuum tube technology is marked by ever-finer grids, so that this relationship can be maintained. Fremlin [Frem39] describes the theory which applies when the grid is closer to the cathode than its pitch.

Figure 10: Zero-volt potential contour as tube approaches cutoff (dimensions in cm)

Figure 10 shows how this applies to a 6SN7, which being an older design does not have especially close spacing. At -5.3V grid potential, the whole cathode is contributing to the plate current. As the grid becomes more negative, "inselbildung" starts - the parts of the cathode directly under the grid wires are in a negative field. By -10V less than half the cathode is still contributing. At -11.4V, the whole cathode is seeing a negative potential, and the tube is truly cut off, i.e. there is no plate current. It can be shown that the effect of inselbildung is to replace the $\frac{3}{2}$ power in Child's Law by a $\frac{5}{2}$ power. Thus at high currents and small grid voltage, the tube obeys a $\frac{3}{2}$ power, but as the grid is made more negative and current reduces, this gradually turns into a $\frac{5}{2}$ law. This is a major reason for the tuck under that plate curves show at large negative grid voltages.

So far this is purely a question of proportion, and not of the absolute size of the tube. Recall however that the space charge creates a virtual cathode typically about 0.1mm ahead of the physical cathode, which further reduces the effective distance to the grid. This distance is independent of the tube geometry. It is 0.1mm whether in an early tube with 2mm from cathode to grid, or in a 1950s design where it may be 0.2mm or less - which places the grid only slightly ahead of the virtual cathode. In fact the virtual cathode is no longer a straight line. Since it is further from the physical cathode at lower current, it will approach the grid wires even closer, forming something close to a mirror image of the 0V potential contour. (This ignores the sideways velocity of the electrons. As far as I know the impact of this has never been analysed in detail, probably because the required computing power only appeared after the tube was considered obsolete). The extreme case of close spacing is the WE417A (or 5842), which achieves a record value of $G_M$ for a small tube (25 mA/V) by very close construction. For this tube, at low currents the virtual cathode actually reaches the plane of the grid. From this point all of the classic mathematical description of triode operation becomes completely irrelevant.

From a practical point of view, at least as far as audio is concerned, the moral of all this is to operate tubes at as high a standing current and as low a bias level (i.e. closer to zero) as is possible for the circuit to operate correctly, so as to keep operation well into the $\frac{3}{2}$ power part of the plate curves and hence reduce distortion, paticularly higher-harmonic distortion

Directly Heated Tubes

Most of the physics behind directly-heated tubes is the same as for indirectly-heated tubes, but there are some differences. First, there is the question of the effective area of the cathode. An accepted formula for this is to use the length of the filament times twice the filament-grid distance [Spang48, p189]

The most significant difference arises because the voltage along the filament is not constant, but varies from one end to the other by the applied filament potential. Although this potential is small, it must be remembered that the effective plate voltage as seen at the cathode (filament) is also small. For example, a 300B operating under quiescent conditions of 350V and 90mA, with 60V on the grid, has a potential as seen at the cathode of around 15V, against a filament voltage of 5V. At the negative extreme of grid voltage, modulated by the signal, this effective voltage will drop close to or even below 5V

When the effective plate voltage is less than the filament voltage, only part of the filament contributes to the plate current, i.e. the part which is still more negative than the filament. Furthermore, the current varies along the filament. The effect of this is that the current becomes dependent on the $\frac{5}{2}$ power of the effective plate voltage, rather than the $\frac{3}{2}$ power. As the plate voltage increases beyond the filament voltage, there is a gradual transition between the $\frac{3}{2}$ power and the $\frac{5}{2}$ power, which is approximately given by the formula [Dow37]:

$I_p=P{V}_{eff}^{\frac{3}{2}}[1-\frac{3}{4}(1+\frac{1}{\mu }){\displaystyle \frac{V_{fil}}{V_{eff}}}]$

where:

$P$ = perveance $V_{eff}$ = effective plate voltage $V_{fil}$ = filament voltage

It is this shift from a $\frac{3}{2}$ law to a $\frac{5}{2}$ law which explains the distinctive tuck under observed in the plate curves for filamentary tubes at high negative grid voltages and low currents. Substituting the above numbers for a typical 300B, the plate current will be reduced by about 25%.

It has been observed [Bench99] that distortion can be measurably reduced with filamentary tubes by lowering the filament voltage to the lowest possible value consistent with avoiding saturation. In fact, in a filamentary tube with close cathode-grid spacing, at low currents the law will follow an even higher power, in theory $\frac{7}{2}$.

Using AC rather than DC for the filaments does not significantly reduce this effect. At any given instant, even with AC heating, there is a potential gradient along the filament (except for the brief moment when the filament voltage passes through zero). Some of the time it is greater than the equivalent DC voltage, and some of the time it is less, but taken through the whole AC cycle the net effect is substantially the same.

Contact Potential

Any two different metals placed in contact with each other generate a potential difference. This is the underlying principle of all batteries, as well as the thermocouple. This difference is due to the different energy levels of the electrons in the two metals, and is called the contact potential of the two metals. The reasons are similar to the work function which determines electron emission, although the two are not the same. In fact, this effect applies even if the two metals are not in contact with each other, applying in this case to the electric field between them. Thus the grid and cathode of a tube, typically made of nickel and barium/strontium oxide respectively, have a small contact potential, which serves to change the effective grid potential. This contact potential is typically less than 0.5V

Transit Time

The electrons must take a finite amount of time to travel from the cathode to the plate. This time is referred to as transit time, and is sometimes invoked to explain various phenomena relating to audio. Transit time did indeed become of practical importance when tubes were first used to build VHF and UHF equipment, and it ultimately sets a limit to the frequencies at which they can usefully operate (in the region 1-2GHz). The transit time can be calculated to be around 1nS from cathode to plate, which at audio frequencies is clearly not relevant.

Multi-Grid Tubes: The Tetrode

The triode was the first amplifying device to be built, but at radio frequencies it suffers from a grave disadvantage because of the Miller Effect, which gives it a large effective input capacitance in the conventional common-cathode circuit. To avoid this, the tetrode was invented, having a second grid (the screen grid) between the triode grid (called the control grid in multi-grid tubes) and the plate. This grid is connected to a positive voltage close to the plate potential, but grounded to high frequencies through a decoupling capacitor. This results in an electrostatic shield which reduces the effective control grid-plate capacitance to a very low value

A secondary effect of the screen grid is to reduce dramatically the influence of the plate voltage on the current flow, since the cathode is shielded from the plate by not one but two grids, and their screening effect is multiplied. As a result, the plate curves of a tetrode are very flat, as seen on the right-hand side of Figure 11. This corresponds to a very high value of plate resistance, as compared to a triode

Some of the current from the cathode goes to the screen grid rather than the plate. The proportion depends on the shielding factor of the screen grid and on the relative potentials of the two electrodes, in much the same way as for a triode operated with a positive grid. It is typically 10-25%.

Figure 11: Plate and screen grid current of true tetrode (UY224) 

Unfortunately the tetrode suffers from a severe problem in practice. The left-hand side of Figure 11 shows that at low plate voltages, the plate curves are extremely non-linear. This is because of secondary emission from the plate. When the screen grid voltage is higher than the plate, electrons emitted from the plate by secondary emission, as it is struck by the energetic primary electrons, are attracted back to the screen grid instead of returning to the plate as occurs in a triode. As a result, a tetrode can only be used if the circuit design is such that this part of the plate curve will not be encountered. Hence, the simple tetrode has not been used, except for high-power transmitting tubes, since the 1930s. There has been no post-WWII small-signal tetrode produced in quantity.

The Pentode

The solution to the tetrode's problem was to introduce a third grid between the screen grid and the plate. Called the suppressor grid, this is always connected to the cathode and hence appears negative both to the plate and to the screen grid. By this means, secondary electrons emitted from both of these electrodes see a field which sends them back where they came from, regardless of the relative potential between the electrodes. Thus the problems of secondary emission are eliminated. The suppressor grid has no effect on the flow of current, since by the time electrons reach it they have been sufficiently accelerated by the screen grid that they simply pass between the grid wires. They are slowed down but not stopped by the grounded suppressor grid

Since the cathode is shielded from the plate by no less than three grids, the effect of plate voltage on current flow is negligible in the pentode, resulting in plate curves that are even flatter than for the tetrode

The Beam Tetrode

The beam tetrode exploits an alternative way of avoiding secondary emission problems, without the manufacturing complexity of using a third grid. It was observed in the 1930s that if the distance from the screen grid to the plate is large enough, the space charge of the electrons flowing in this region can depress the potential substantially without having an actual electrode. This is the basis of the beam tetrode. The reduced potential in this region serves the same function as the suppressor grid, causing secondary electrons to turn back to their origin and avoiding their effect on the electrode currents

To make this effect work in practice, three things are necessary. First, the electron flow must be confined to a narrow beam, otherwise the space charge spreads out parallel to the plate and the effect is lost. This is achieved by the beam electrodes, carefully shaped plates connected to the cathode and placed either side of the electron path between the screen grid and the plate. Second, the electrons must flow in clean sheets, which requires that the grid wires of the control grid and the screen grid be in line. This is not surprisingly a tricky manufacturing problem. Finally, the electrode dimensions and spacing must be carefully calculated

Although there are slight differences in the detailed operation of pentodes and beam tetrodes, for most practical purposes they can be considered as the same. Indeed, there are tube types which some manufacturers built one way, and others in the other way. Eric Barbour [Barb97] mentions that the EL84/6BQ5 was made in both ways.

Beyond the Pentode

To build an amplifier, nothing beyond the pentode is needed. But for some other special purposes, extra grids were added. In particular, hexodes (four grids) and heptodes (five grids) were used as frequency changers in radios and televisions. In these, one grid carries the RF signal, and one carries the oscillator frequency that intermodulates with the RF signal to generate the IF signal at a different carrier frequency.

Common frequency changers such as the ECH80/6AN7 put a triode in the same envelope, to provide the oscillator function.

With a heptode or even an octode (six grids), such as the EK90/6BE6, the oscillator could be combined in the same grid structure, avoiding the need for a separate tube or element.

The ultimate multi-grid tube was the EQ80/6BE7 nonode, with no less than seven grids. This was designed by Philips very specifically for use as an advanced FM detector, and seems not have had widespread use. It must have been very challenging to build, considering the tiny clearances involved.

Multi-Element Tubes

The electronic structure inside the glass envelope of a tube is generally quite small compared to the space available. It was therefore natural to put two or more such elements in a single envelope, especially where the combination satisfied some specific use case. The major limit to this was the number of pins available for the external connections. Typically each element had its own pins, with only the filament connection being shared between them. 

Common combinations included:

• two independent triodes: 6SL7, 6SN7, ECC81/12AU7 and so on
• a triode amplifier and a pentode output stage: ECF80/6BL8, ECL80/6BE6
• a triode oscillator and a hexode frequency changer: ECH80/6BE6

Sometimes, certain connections were shared on a common pin. Often the cathodes would be wired this way, as in the ECL80/6BE6.

The ultimate multi-element tube was the ECLL80, which contained everything needed for a complete push-pull audio output stage: a triode phase splitter, and two beam pentodes for the output stage. This was only possible with some clever pin-sharing, very specifically chosen for the intended use.

Color television greatly increased the number of tubes required, with three separate color video signals. In response, GE developed the Compactron tube in 1961, which used a new 12-pin base combined with a larger-diameter envelope. This allowed three triodes, or two pentodes, to be fitted into a single tube. However televisions rapidly moved to use transistors in the 1960s, so these had a very limited production life.

Spice Modelling

Today nobody would turn on their soldering iron without first having built a comprehensive Spice model of an analog circuit. Naturally, such models were not available in the heyday of vacuum tubes, since they depend on readily available powerful computing facilities. And generally, tube circuits are simple enough that the models do not add a great deal of understanding.

Nevertheless, people are interested in using Spice for tubes. The difficulty is in obtaining sufficiently accurate Spice models for them. A semiconductor manufacturer is obliged to produce these models for every part they produce, but the tube manufacturers have long since gone, or at least lost interest. As shown here, the transfer characteristics of a tube are far from simple, once the simple $\frac{3}{2}$ rule is left behind. It was the intent of creating such models that led the author down the path of investigating all the theory in this collection of posts, but nothing sufficiently robust emerged.

The most likely path is a combination of empirical data with a theory-based model that can integrate it. Today, Artifical Intelligence would most probably be a key part of such a success. But that would be a brand-new research project.

The best models currently available are from [Koren03], which indeed combine an empirically-derived mathematical model with empirical data.

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Tubes 201 - How Vacuum Tubes Really Work, Part 7: Noise

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Thermal Noise

All electronic, and indeed electrical, devices produce noise. The most fundamental, and unavoidable, form of noise is called thermal noise or sometimes shot noise. It occurs because the flow of electricity is actually due to individual electrons. Even though the number of electrons is huge, there are still statistically predictable fluctuations, just like traffic on the highway. Because it is random, this noise occurs equally at all frequencies. The noise voltage developed by any conductor or resistor is given by:

$e_{noise}=2\sqrt{kTR{\mathrm{\Delta }}_f}$

where:

$e_{noise}$ = noise voltage $k$ = Boltzmann's constant, 1.38·10-23 $T$ = temperature (°K) $R$ = resistance ${\mathrm{\Delta }}_f$ = bandwidth

For example a 1kΩ resistor at room temperature (approx. 300°K), across the audio bandwidth from 0-20kHz, produces a noise voltage of about 0.6µV. When dealing with very small signals, such as a received radio signal or a phono pickup, this is a significant amount of noise

Thermal Noise in Tubes

There is a simple way to calculate the thermal noise in a triode. The noise produced by the tube is equivalent to a resistor in series with the grid, at room temperature, whose value is given by:

$R_{noise}={\displaystyle \frac{2.5}{G_m}}$

where:

$R_{noise}$ = equivalent noise resistance

In other words, the noise produced by a tube is inversely proportional to $G_m$. This directly explains the later interest in high $G_m$ tubes such as the WE417A. This tube was intended for the first stages of sensitive VHF and UHF receivers, where minimum noise is a critical feature. It has also been considered for sensitive phono stages, though its other noise sources (see below) may be an issue.

In addition to thermal noise, tubes generate noise in two other ways, called flicker noise and separation noise.

Flicker Noise

The second source of noise in tubes is flicker noise, also called 1/f noise which clearly describes its nature: it is noise which decreases with increasing frequency. It is of no interest for radio work, but has obvious importance for audio since most of the noise lies in the audio band. It is particularly important for phono stages, since the RIAA correction, by attenuating higher frequencies, boosts the contribution of noise at lower frequencies

Flicker noise is caused by variations in cathode emission due to movement of atoms within the cathode structure. In oxide-coated cathodes, it occurs primarily at the interface between the oxide layer and the base metal of the cathode, which is generally a nickel alloy. Some alloys are much better than others in this respect, showing a difference of a factor of 20 or more [Smullin59, p65]. A high silicon content increases flicker noise, but unfortunately has advantages in the manufacturing process and so tended to be widely used. The cathode alloy was chosen by each manufacturer, and does not form part of the specification of a particular tube type, which explains the wide variation in tubes from different manufacturers. Smullin [Smullin59] indicates that European manufacturers tended to use alloys which are better in this respect

Pure tungsten filaments generate flicker noise in a different way, resulting in a noise spectrum which is $1/f^2$ rather than just $1/f$ - in other words, the audio component is even more predominant.

Partition Noise

The third source of noise applies only to tetrodes and pentodes, and explains why pentodes are noisier than triodes. The presence of the positive screen grid means that some of the current (typically 10-20%) from the cathode goes to the screen grid rather than the plate. However this division of current fluctuates randomly, just as the current itself does. This very slight random variation in the plate current is called partition noise

The effect of partition noise is to change the equivalent noise resistance from the simple formula given above to:

$$R_{noise}=\frac{2.5}{G_m}(1+8\frac{I_{screen}}{G_m})$$

In practice, this results in three to five times the noise of the equivalent triode. Connecting a tetrode or pentode as a triode eliminates partition noise, since now the two current flows are recombined.

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