distributed element filter design.[7]

The scheme presented in the table is known as the impedance analogy. Circuit diagrams produced using this analogy match the electrical impedance of the mechanical system seen by the electrical circuit, making it intuitive from an electrical engineering standpoint. There is also the mobility analogy,[n 1] in which force corresponds to current and velocity corresponds to voltage. This has equally valid results but requires using the reciprocals of the electrical counterparts listed above. Hence, M → C, S → 1/L, D → G where G is electrical conductance, the inverse of resistance. Equivalent circuits produced by this scheme are similar, but are the dual impedance forms whereby series elements become parallel, capacitors become inductors, and so on.[4] Circuit diagrams using the mobility analogy more closely match the mechanical arrangement of the circuit, making it more intuitive from a mechanical engineering standpoint.[5] In addition to their application to electromechanical systems, these analogies are widely used to aid analysis in acoustics.[6]
Any mechanical component will unavoidably possess both mass and stiffness. This translates in electrical terms to an LC circuit, that is, a circuit consisting of an inductor and a capacitor, hence mechanical components are resonators and are often used as such. It is still possible to represent inductors and capacitors as individual lumped elements in a mechanical implementation by minimising (but never quite eliminating) the unwanted property. Capacitors may be made of thin, long rods, that is, the mass is minimised and the compliance is maximised. Inductors, on the other hand, may be made of short, wide pieces which maximise the mass in comparison to the compliance of the piece.[7]
Mechanical parts act as a transmission line for mechanical vibrations. If the wavelength is short in comparison to the part then a lumped element model as described above is no longer adequate and a distributed element model must be used instead. The mechanical distributed elements are entirely analogous to electrical distributed elements and the mechanical filter designer can utilise the techniques of electrical distributed element filter design.[7]






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EU leaders meeting amid eurozone jitters

The German chancellor (left) does not want to pour more euros into the current EU rescue fund
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Global Economy

EU austerity drive country by country
In graphics: Eurozone's woes
Q&A: Why bond markets matter
Europe's bad debt 'dominoes'?
Concerns about the stability of the eurozone are set to dominate a meeting of European leaders in Brussels.

The two-day summit is expected to see an agreement to set up a permanent system for rescuing countries that get heavily into debt.

But there is still much debate about how such a system should operate.

Meanwhile concern over Spain's financial stability continued as it was forced to pay a higher rate of interest in a government bond sale.

Spain has been under financial market scrutiny since the Irish Republic was forced to take an aid package of 85bn euros (£72bn; $113bn) last month.

That bail-out followed the 110bn-euro rescue of Greece in May.

Arriving at the summit, Sweden's Prime Minister Fredrik Reinfeldt stressed that beyond crisis management there was a long-term need for EU countries to reform labour markets and boost competitiveness.

Greece's Prime Minister George Papandreou said "the challenge is a collective one now - more integration... and all have to live up to their responsibilities".

'Succeed together'
Issues on the agenda in Brussels include:

How to change the EU's Lisbon Treaty to allow changes to create a permanent stability mechanism for eurozone members
Whether to increase the eurozone's 750bn-euro temporary bail-out fund, the European Financial Stability Facility (EFSF)
The possibility of creating pan-European bonds to boost confidence in the euro.
But even assuming that leaders do agree to the way countries are helped, the slow pace of politics in Brussels means a permanent stability arrangement will not come into force until 2013, says BBC Europe correspondent Matthew Price.

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“
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The lesson of the last year is - it's best to be prepared for the worst”


Andrew Walker
Economics correspondent, BBC World Service
How private investors will have to share the pain
In the meantime they will have to rely on the current temporary mechanism that has already been used to rescue Greece and the Irish Republic, he added.

And analysts have expressed concern that talks will not address a key issue - whether or not investors who have bought bonds in struggling euro nations will have to lose money, or in the language of the financial world, take a "haircut", on their investment between now and 2013.

This was causing "uncertainty" in financial markets, said Carsten Brzeski, a senior analyst at ING.

"This is an inconsistency. The politicians need to address this insolvency issue in the period between now and 2013," he told the BBC.

German caution
French Foreign Minister Michele Alliot-Marie said that the EU had to stop speculators from attacking eurozone countries and would adopt ways to do that at the summit.

And separately the Prime Minister of Luxembourg, Jean-Claude Juncker, said European leaders were determined to do everything to ensure the eurozone's financial stability.

On Wednesday, German Chancellor Angela Merkel stressed Berlin's commitment to help its European partners, pledging that: "Nobody in Europe will be abandoned. Europe will succeed together."

But she has been an opponent of some suggested actions, including increasing the eurozone's euro bail-out fund or introducing euro bonds.

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“
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In truth Europe does not yet have a convincing answer to the crisis and the financial markets know it”


Gavin Hewitt
BBC Europe editor
Hewitt: The euro crisis that defies answers
Concerns reflected
In its latest bond auction, Madrid managed to raise 2.4bn euros.

But the yield on the Spanish bonds - essentially the interest rate which the government must pay in order to borrow money - was higher than that on previous auctions of similar bonds.

The Spanish treasury sold 1.8bn euros worth of 10-year bonds at an average interest rate of 5.4% - up from 4.6% in the last such auction in November,

And it was forced to pay a rate of 6% to sell 618m euros in 15-year bonds, up from 4.5% in October.

The rising cost of borrowing reflects investors' concern about the outlook for the Spanish economy and its banking sector in particular.

Madrid insists it will not need to apply for a bail-out from the EFSF - the temporary rescue scheme funded by the EU and International Monetary Fund.

Downgrade threat
While the demand for Spanish bonds remained oversubscribed, concerns remained about Spain's ability to get affordable funding to refinance its debts and support its banks, said Kathleen Brooks, research director at Forex.com.

And this had wider implications for the single currency, she added.

"Spain is the canary in the coal mine for the survival of the eurozone," Ms Brooks said.

On Wednesday, ratings agency Moody's said it was reviewing Spain's credit rating with a view to downgrading it - warning of problems the country faced in refinancing its debts next year.

Moody's had already cut Spain's sovereign debt rating from the top, triple-A rating to Aa1 in September.







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