Thermal solar systems and components - Custom built systems - Part 3: Performance test methods for solar water heater stores

This European Standard specifies test methods for the performance characterization of stores which are intended for use in small custom built systems as specified in EN 12977-1.
Stores tested according to this document are commonly used in solar hot water systems. However, the thermal performance of all other thermal stores with water as a storage medium can also be assessed according to the test methods specified in this document.
The document applies to stores with a nominal volume between 50 l and 3 000 l.
This document does not apply to combistores. Performance test methods for solar combistores are specified in EN 12977-4.

Thermische Solaranlagen und ihre Bauteile - Kundenspezifisch gefertigte Anlagen - Teil 3: Leistungsprüfung von Warmwasserspeichern für Solaranlagen

Diese Europäische Norm legt Prüfverfahren für die Beschreibung der Leistung von Warmwasserspeichern (im Folgenden Speicher genannt) fest, die zur Verwendung in kleinen kundenspezifisch gefertigten Solaranlagen nach EN 12977-1:2018 bestimmt sind.
Die nach diesem Dokument geprüften Speicher werden häufig in thermischen Solaranlagen verwendet. Jedoch kann auch die thermische Leistung aller anderen Wärmespeicher, bei denen Wasser als Speichermedium zum Einsatz kommt, nach den in diesem Dokument festgelegten Prüfverfahren bewertet werden.
Dieses Dokument gilt für Speicher mit einem Nennvolumen zwischen 50 l und 3 000 l.
Dieses Dokument gilt nicht für Kombispeicher. Die Verfahren zur Leistungsprüfung von Solar-Kombispeichern sind in EN 12977-4:2018 festgelegt.

Installations solaires thermiques et leurs composants - Installations assemblées à façon - Partie 3 : Méthodes d'essai des performances des dispositifs de stockage des installations de chauffage solaire de l'eau

La présente Norme européenne spécifie des méthodes d'essai pour la caractérisation des performances des dispositifs de stockage destinés à être utilisés dans de petites installations assemblées à façon, comme spécifié dans l’EN 12977-1:2018.
Les dispositifs de stockage soumis à essai conformément au présent document sont couramment utilisés dans les installations de chauffage solaires. Toutefois, les performances thermiques de tous les autres dispositifs de stockage thermique où l’eau est utilisée comme milieu de stockage peuvent également être évaluées conformément aux méthodes d’essai spécifiées dans le présent document.
Le document s’applique aux dispositifs de stockage dont le volume nominal est compris entre 50 l et 3 000 l.
Le présent document ne s’applique pas aux dispositifs de stockage combinés. Les méthodes d’essai relatives aux performances des dispositifs de stockage combinés sont spécifiées dans l’EN 12977-4:2018.

Toplotni sončni sistemi in sestavni deli - Neserijsko izdelani sistemi - 3. del: Preskusne metode delovanja hranilnikov toplote, ogrevanih s soncem

Ta evropski standard določa preskusne metode za delovanje hranilnikov, ki so namenjeni za uporabo v majhnih neserijsko izdelanih sistemih v skladu s standardom EN 12977-1.
Hranilniki, ki se preskušajo v skladu s tem dokumentom, se običajno uporabljajo za sončne toplovodne sisteme. Vendar se lahko na podlagi preskusnih metod iz tega dokumenta oceni tudi toplotna učinkovitost vseh drugih hranilnikov toplote, ki kot sredstvo shranjevanja uporabljajo vodo.
Dokument se uporablja za hranilnike z nazivno prostornino od 50 l do 3000 l.
Ta dokument se ne uporablja za kombinirane hranilnike. Preskusne metode za delovanje sončnih kombiniranih hranilnikov so določene v standardu EN 12977-4.

General Information

Status
Published
Public Enquiry End Date
19-Sep-2017
Publication Date
20-Aug-2018
Technical Committee
Current Stage
6060 - National Implementation/Publication (Adopted Project)
Start Date
17-Apr-2018
Due Date
22-Jun-2018
Completion Date
21-Aug-2018

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2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.PThermische Solaranlagen und ihre Bauteile - Kundenspezifisch gefertigte Anlagen - Teil 3: Leistungsprüfung von Warmwasserspeichern für SolaranlagenInstallations solaires thermiques et leurs composants - Installations assemblées à façon - Partie 3 : Méthodes d'essai des performances des dispositifs de stockage des installations de chauffage solaire de l'eauThermal solar systems and components - Custom built systems - Part 3: Performance test methods for solar water heater stores91.140.65Oprema za ogrevanje vodeWater heating equipment91.140.10Sistemi centralnega ogrevanjaCentral heating systems27.160Solar energy engineeringICS:Ta slovenski standard je istoveten z:EN 12977-3:2018SIST EN 12977-3:2018en,fr,de01-september-2018SIST EN 12977-3:2018SLOVENSKI

STANDARDSIST EN 12977-3:20121DGRPHãþD
SIST EN 12977-3:2018
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN 12977-3
April
t r s z ICS
t yä s x râ
{ sä s v rä s râ
{ sä s v rä x w Supersedes EN
s t { y yæ uã t r s tEnglish Version
Thermal solar systems and components æ Custom built systems æ Part

uã Performance test methods for solar water heater stores Installations solaires thermiques et leurs composants æInstallations assemblées à façon æ Partie

u ã Méthodes d 5essai des performances des dispositifs de stockage des installations de chauffage solaire de l 5eau

Thermische Solaranlagen und ihre Bauteile æ Kundenspezifisch gefertigte Anlagen æ Teil

uã Leistungsprüfung von Warmwasserspeichern für Solaranlagen This European Standard was approved by CEN on

t { October
t r s yä

egulations which stipulate the conditions for giving this European Standard the status of a national standard without any alterationä Upætoædate lists and bibliographical references concerning such national standards may be obtained on application to the CENæCENELEC Management Centre or to any CEN memberä

translation under the responsibility of a CEN member into its own language and notified to the CENæCENELEC Management Centre has the same status as the official versionsä

CEN members are the national standards bodies of Austriaá Belgiumá Bulgariaá Croatiaá Cyprusá Czech Republicá Denmarká Estoniaá Finlandá Former Yugoslav Republic of Macedoniaá Franceá Germanyá Greeceá Hungaryá Icelandá Irelandá Italyá Latviaá Lithuaniaá Luxembourgá Maltaá Netherlandsá Norwayá Polandá Portugalá Romaniaá Serbiaá Slovakiaá Sloveniaá Spainá Swedená Switzerlandá Turkey and United Kingdomä

EUROPEAN COMMITTEE FOR STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre:
Rue de la Science 23,
B-1040 Brussels

t r s z CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Membersä Refä Noä EN

s t { y yæ uã t r s z ESIST EN 12977-3:2018

EN 12977-3:2018 (E) 2 Contents Page European foreword ....................................................................................................................................................... 4 Introduction .................................................................................................................................................................... 5 1 Scope .................................................................................................................................................................... 6 2 Normative references .................................................................................................................................... 6 3 Terms and definitions ................................................................................................................................... 6 4 Symbols and abbreviations ...................................................................................................................... 11 5 Store classification ....................................................................................................................................... 12 6 Laboratory store testing ............................................................................................................................ 12 6.1 Requirements on the testing stand ........................................................................................................ 12 6.1.1 General ............................................................................................................................................................. 12 6.1.2 Measured quantities and measuring procedure .............................................................................. 15 6.2 Installation of the store .............................................................................................................................. 16 6.2.1 Mounting ......................................................................................................................................................... 16 6.2.2 Connection ...................................................................................................................................................... 16 6.3 Test and evaluation procedures ............................................................................................................. 16 6.3.1 General ............................................................................................................................................................. 16 6.3.2 Test sequences .............................................................................................................................................. 18 6.3.3 Data processing of the test sequences .................................................................................................. 29 7 Store test combined with a system test according to ISO 9459-5 ............................................... 30 8 Store test according to EN 12897 ........................................................................................................... 31 9 Determination of store parameters by means of “up- and down-scaling” .............................. 31 9.1 General ............................................................................................................................................................. 31 9.2 Requirements ................................................................................................................................................ 31 9.3 Determination of store parameters ...................................................................................................... 32 9.3.1 Thermal capacity of store ......................................................................................................................... 32 9.3.2 Height of store ............................................................................................................................................... 32 9.3.3 Determination of heat capacity rate ..................................................................................................... 32 9.3.4 Relative heights of the connections and the temperature sensors ............................................ 32 9.3.5 Heat exchangers ........................................................................................................................................... 32 9.3.6 Parameter describing the degradation of thermal stratification during stand-by .............. 32 9.3.7 Parameter describing the quality of thermal stratification during direct discharge ......... 33 10 Test report ...................................................................................................................................................... 33 10.1 General ............................................................................................................................................................. 33 10.2 Description of the store ............................................................................................................................. 33 10.3 Test results ..................................................................................................................................................... 34 10.4 Parameters for the simulation ................................................................................................................ 35 Annex A (normative)

Store model benchmark tests .................................................................................... 36 A.1 General ............................................................................................................................................................. 36 A.2 Temperature of the store during stand-by ......................................................................................... 36 A.3 Heat transfer from heat exchanger to store ....................................................................................... 36 Annex B (normative)

Verification of store test results ................................................................................ 38 SIST EN 12977-3:2018

EN 12977-3:2018 (E) 3 B.1 General ............................................................................................................................................................. 38 B.2 Test sequences for verification of store test results ........................................................................ 38 B.2.1 General ............................................................................................................................................................. 38 B.2.2 Verification sequences from measurements on a store testing stand ...................................... 38 B.2.2.1 General ............................................................................................................................................................. 38 B.2.2.2 Stores of all groups ....................................................................................................................................... 39 B.2.2.2.1 Connection of the storage device to the testing stand ............................................................ 39 B.2.2.2.2 Group 1 ..................................................................................................................................................... 39 B.2.2.2.3 Group 2 ..................................................................................................................................................... 40 B.2.2.2.4 Group 3 ..................................................................................................................................................... 41 B.2.2.2.5 Group 4 ..................................................................................................................................................... 42 B.2.2.3 Stores with auxiliary heat exchanger(s) .............................................................................................. 43 B.2.2.4 Stores with electrical auxiliary heating element(s) ......................................................................... 44 B.2.3 Test sequences obtained during a whole system test according to ISO 9459-5 .................... 45 B.3 Verification procedure ............................................................................................................................... 45 B.3.1 General ............................................................................................................................................................. 45 B.3.2 Error in transferred energies ................................................................................................................... 45 B.3.3 Error in transferred power ....................................................................................................................... 46 Annex C (normative)

Benchmarks for the parameter identification ...................................................... 47 Annex D (informative)

Requirements for the numerical store model ................................................... 48 D.1 General ............................................................................................................................................................. 48 D.2 Assumptions ................................................................................................................................................... 48 D.3 Calculation of energy balance .................................................................................................................. 48 Annex E (informative)

Determination of hot water comfort ..................................................................... 50 Annex F (informative)

Implementation for Ecodesign and Energy Labelling ..................................... 51 F.1 Standing loss ................................................................................................................................................... 51 F.2 Nominal store volume ................................................................................................................................. 51 F.3 Volume of the non-solar heat storage ................................................................................................... 51 Annex ZA (informative)

Relationship between this European Standard and the energy labelling requirements of Commission Delegated Regulation (EC) No 811/2013 aimed to be covered ..................................................................................................................................... 52 Annex ZB (informative)

Relationship between this European Standard and the energy labelling requirements of Commission Delegated Regulation (EC) No 812/2013 aimed to be covered ..................................................................................................................................... 53 Annex ZC (informative)

Relationship between this European Standard and the ecodesign requirements of Commission Regulation (EC) No 814/2013 aimed to be covered ............. 54 Bibliography ................................................................................................................................................................. 55 SIST EN 12977-3:2018

EN 12977-3:2018 (E) 4 European foreword This document (EN 12977-3:2018) has been prepared by Technical Committee CEN/TC 312 “Thermal solar systems and components”, the secretariat of which is held by ELOT. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2018, and conflicting national standards shall be withdrawn at the latest by October 2018. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights. This document supersedes EN 12977-3:2012. This document has been prepared under the Mandate M/534 “Standardisation request to the European standardisation organisations pursuant to Article 10(1) of Regulation (EU) No 1025/2012 of the European Parliament and of the Council in support of implementation of Commission Regulation (EU) No 814/2013 of 2 August 2013 implementing Directive 2009/125/EC of the European Parliament and of the Council with regard to ecodesign requirements for water heaters and hot water storage tanks and Commission Delegated Regulation (EU) No 812/2013 of 18 February 2013 supplementing Directive 2010/30/EU of the European Parliament and of the Council with regard to the energy labelling of water heaters, hot water storage tanks and packages of water heater and solar device” which was given to CEN by the European Commission and the European Free Trade Association. For relationship with EU Directive(s), see informative Annex ZA, ZB and ZC, which are integral parts of this document. EN 12977 is currently composed with the following parts: — Thermal solar systems and components — Custom built systems — Part 1: General requirements for solar water heaters and combisystems; — Thermal solar systems and components — Custom built systems — Part 2: Test methods for solar water heaters and combisystems; — Thermal solar systems and components — Custom built systems — Part 3: Performance test methods for solar water heater stores; — Thermal solar systems and components — Custom built systems — Part 4: Performance test methods for solar combistores; — Thermal solar systems and components — Custom built systems — Part 5: Performance test methods for control equipment. According to the CEN-CENELEC Internal Regulations, the national standards organisations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. SIST EN 12977-3:2018

EN 12977-3:2018 (E) 5 Introduction The test methods for stores of solar heating systems as described in this European Standard are required for the determination of the thermal performance of small custom built systems as specified in EN 12977-1:2018. The test method described in this European Standard delivers a complete set of parameters, which are needed for the simulation of the thermal behaviour of a store being part of a small custom built solar heating system. For the determination of store parameters such as the thermal capacity and the heat loss rate, the method standardized in EN 12897 can be used as an alternative. NOTE 1 The already existing test methods for stores of conventional heating systems are not sufficient with regard to solar heating systems. This is due to the fact that the performance of solar heating systems depends much more on the thermal behaviour of the store (e.g. stratification, heat losses), than conventional systems do. Hence, this separate document for the performance characterization of stores for solar heating systems is needed. NOTE 2 For additional information about the test methods for the performance characterization of stores, see [1] in Bibliography. SIST EN 12977-3:2018

EN 12977-3:2018 (E) 6 1 Scope This European Standard specifies test methods for the performance characterization of stores which are intended for use in small custom built systems as specified in EN 12977-1:2018. Stores tested according to this document are commonly used in solar heating systems. However, the thermal performance of all other thermal stores with water as a storage medium can also be assessed according to the test methods specified in this document. The document applies to stores with a nominal volume between 50 l and 3 000 l. This document does not apply to combistores. Performance test methods for solar combistores are specified in EN 12977-4:2018. 2 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 12828, Heating systems in buildings — Design for water-based heating systems EN 12897, Water supply - Specification for indirectly heated unvented (closed) storage water heaters EN ISO 9488:1999, Solar energy - Vocabulary (ISO 9488:1999) ISO 9459-5, Solar heating — Domestic water heating systems — Part 5: System performance characterization by means of whole-system tests and computer simulation 3 Terms and definitions For the purposes of this document, the terms and definitions given in EN ISO 9488:1999 and the following apply. 3.1 ambient temperature mean value of the temperature of the air surrounding the store 3.2 charge process of transferring energy into the store by means of a heat source 3.3 charge connection pipe connection used for charging the storage device 3.4 combistore one store used for both domestic hot water preparation and space heating SIST EN 12977-3:2018

EN 12977-3:2018 (E) 7 3.5 conditioning process of creating a uniform temperature inside the store by discharging the store with ,Diϑ = 20 °C untl a steady state s reached Note 1 to entry: The condtonng at the begnnng of a test sequence s ntended to provde a well-defned ntal system state, .e. a unform temperature n the entre store. 3.6 constant charge power cP charge power which is achieved when the mean value cP over the perod of 0,5 reduced charge volumes (see 3.33) s wthn cP ± cP × 0,1 Note 1 to entry: The symbol ”~” above a certan value ndcates that the correspondng value s a mean value. 3.7 constant inlet temperature ,ϑxi temperature which is achieved during charge (x = C) or discharge (x = D), if the mean value ,xiϑ over the perod of 0,5 “reduced charge/dscharge volume” (see 3.33) s wthn (,xiϑ ± 1) °C Note 1 to entry: The symbol ”~” above a certan value ndcates that the correspondng value s a mean value. 3.8 constant flow rate V flow rate which is achieved when the mean value of V over the perod of 0,5 “reduced charge/dscharge volumes” (see 3.33) s wthn V ± V × 0,1 Note 1 to entry: The symbol ”~” above a certan value ndcates that the correspondng value s a mean value. 3.9 dead volume/dead capacity volume/capacity of the store which is only heated due to heat conduction (e.g. below a heat exchanger) 3.10 direct charge/discharge transfer or removal of thermal energy in or out of the store, by directly exchanging the fluid in the store 3.11 discharge process of decreasing thermal energy inside the store caused by the hot water load 3.12 discharge connection pipe connection used for discharging the storage device SIST EN 12977-3:2018

EN 12977-3:2018 (E) 8 3.13 double port corresponding pair of inlet and outlet connections for direct charge/discharge of the store Note 1 to entry: Often, the store is charged or discharged via closed or open circuits that are connected to the store through double ports. 3.14 effective volume/effective capacity volume/capacity which is involved in the heat storing process if the store is operated in a usual way 3.15 electrical (auxiliary) heating electrical heating element immersed into the store 3.16 external auxiliary heating auxiliary heating device located outside the store. The heat is transferred to the store by direct or indirect charging via a charge circuit. The external auxiliary heating is not considered as part of the store under test 3.17 heat loss capacity rate (UA)s,a overall heat loss of the entire store during stand-by per K of the temperature difference between the medium store temperature and the ambient air temperature 3.18 heat transfer capacity rate thermal power transferred per K of the temperature difference 3.19 immersed heat exchanger heat exchanger which is completely surrounded with the fluid in the store 3.20 indirect charge/discharge transfer or removal of thermal energy into or out of the store, via a heat exchanger 3.21 load heat output of the store during discharge. The load is defined as the product of the mass, specific thermal capacity and temperature increase of the water as it passes the solar heating system 3.22 mantle heat exchanger heat exchanger mounted to the store in such a way that it forms a layer between the fluid in the store and ambient SIST EN 12977-3:2018

EN 12977-3:2018 (E) 9 3.23 measured energy Qx,m time integral of the measured power over one or more test sequences, excluding time periods used for conditioning at the beginning of the test sequences 3.24 measured power Px,m power calculated from measured volume flow rate as well as measured inlet and outlet temperatures 3.25 measured store heat capacity measured difference in energy of the store between two steady states on different temperature levels, divided by the temperature difference between these two steady states 3.26 mixed state when the local store temperature is not a function of the vertical store height 3.27 model parameter parameter used for quantification of a physical effect, if this physical effect is implemented in a mathematical model in a way which is not analogous to its appearance in reality, or if several physical effects are lumped in the model (e.g. a stratification number) 3.28 nominal flow rate nV nominal volume of the entire store divided by 1 h 3.29 nominal heating power Pn nominal volume of the entire store multiplied by 10 W/l 3.30 nominal volume Vn fluid volume of the store; determined as described in formula (F.2) 3.31 predicted energy Qxp time integral of the predicted power over one or more test sequences, excluding time periods used for conditioning at the beginning of the test sequences SIST EN 12977-3:2018

EN 12977-3:2018 (E) 10 3.32 predicted power Pxp power calculated from measured volume flow rate, as well as measured inlet temperature and calculated outlet temperature Note 1 to entry: The outlet temperature is predicted by numerical simulation. 3.33 reduced charge/discharge volume integral of a charge/discharge flow rate divided by the store volume 3.34 stand-by state of operation in which no energy is deliberately transferred to or removed from the store 3.35 stand-by heat loss capacity rate (UA)sb,s,a heat loss capacity rate of the store during stand-by 3.36 steady state state of operation at which at charge or discharge during 0,5 “reduced charge/discharge volume” (see 3.33) the standard deviation of the temperature difference between store inlet and store outlet temperatures of the charging/discharging circuit is lower than 0,1 K Note 1 to entry: In cases of an isothermal charged store, constant temperature differences between the inlet and outlet temperatures of the discharge circuit may occur during the discharge of the first store volume before the outlet temperature drops rapidly. This state is not considered as steady-state. 3.37 store temperature temperature of the store medium 3.38 stratified state when thermal stratification is present inside the store 3.39 stratified charging increase of thermal stratification in the store during charging 3.40 stratifier device that enables stratified charging of the store. Commonly used stratifiers are e.g. convection chimneys or pipes with radial holes 3.41 theoretical store heat capacity sum over all thermal capacities mi × cp,i of the entire store (fluid, store material, heat exchangers) having part of the heat store process SIST EN 12977-3:2018

EN 12977-3:2018 (E) 11 3.42 thermal stratification state when the local store temperature is a function of the vertical store height, with the temperature decreasing from top to bottom 3.43 transfer time tx,f time period during which energy is transferred through the connections for charge (x = C) or discharge (x = D). The transfer time is calculated over one or more test sequences, excluding time periods used for conditioning at the beginning of the test sequences 4 Symbols and abbreviations For the purposes of this document, the following symbols and abbreviations apply. Cs thermal capacity of the entire store, in J/K cp specific heat capacity, in J/(kg K) Pn nominal heating power, in W Px,m measured power transferred through the charge (x = C) or discharge (x = D) circuit, in W Px,p predicted power transferred through the charge (x = C) or discharge (x = D) circuit, in W Qx,m measured energy transferred through the charge (x = C) or discharge (x = D) circuit, in J Qx,p predicted energy transferred through the charge (x = C) or discharge (x = D) circuit, in J tst time required to achieve a steady-state, in s tx,f transfer time for charging (x = C) or discharging (x = D), in s (UA)hx,s heat transfer capacity rate between heat exchanger and store, in W/K (UA)s,a heat loss capacity rate of the store, in W/K (UA)sb,s,a stand-by heat loss capacity rate of the store, in W/K Vn nominal volume of the store, in l nV nominal flow rate, in l/h xV constant flow rate of the charge (x = C) or discharge (x = D) circuit, in l/h Ím mean logarithmic temperature difference, in K Ía ambient temperature, in °C Ís store temperature, in °C Íx,i inlet temperature of the charge (x = C) or discharge (x = D) circuit, in °C ,xiϑ constant inlet temperature of the charge (x = C) or discharge (x = D) circuit, in °C Íx,o outlet temperature of the charge (x = C) or discharge (x = D) circuit, in °C SIST EN 12977-3:2018

EN 12977-3:2018 (E) 12 x,P relative error in mean power transferred during charge (x = C) or discharge (x = D), in % x,Q relative error in energy transferred during charge (x = C) or discharge (x = D), in %

density, in kg/m3 5 Store classification Hot water stores are classified by distinction between different charge and discharge modes. Five groups are defined as shown in Table 1. Table 1 — Classification of the stores Group Charge mode Discharge mode 1 direct direct 2 indirect direct 3 direct indirect 4 indirect indirect 5 stores that cannot be assigned to groups 1 to 4 NOTE All stores can have one or more additional electrical auxiliary heating elements. 6 Laboratory store testing 6.1 Requirements on the testing stand 6.1.1 General The hot water store shall be tested separately from the whole solar system on a store-testing stand. The testing stand configuration shall be determined by the classification of hot water stores as described in Clause 5. An example of a representative hydraulic testing stand configuration is shown in Figure 1 and Figure 2. The circuits are intended to simulat

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