Question: What was the dynasty, that birthed the empire, that had the Electorate of Baden as one of its states?

full_context: Document 1: Kingdom of Bavaria: The Kingdom of Bavaria (; ) was a German state that succeeded the former Electorate of Bavaria in 1805 and continued to exist until 1918. The Bavarian Elector Maximilian IV Joseph of the House of Wittelsbach became the first King of Bavaria in 1805 as Maximilian I Joseph. The crown would go on being held by the Wittelsbachs until the kingdom came to an end in 1918. Most of Bavaria's present-day borders were established after 1814 with the Treaty of Paris, in which Bavaria ceded Tyrol and Vorarlberg to the Austrian Empire while receiving Aschaffenburg and Würzburg. With the unification of Germany into the German Empire in 1871, the kingdom became a federal state of the new Empire and was second in size, power, and wealth only to the leading state, the Kingdom of Prussia. In 1918, Bavaria became a republic, and the kingdom was thus succeeded by the current Free State of Bavaria.
Document 2: East Prussia: The Administrator of Prussia, the grandmaster of the Teutonic Order Maximilian III, son of emperor Maximilian II died in 1618. When Maximilian died, Albert's line died out, and the Duchy of Prussia passed to the Electors of Brandenburg, forming Brandenburg-Prussia. Taking advantage of the Swedish invasion of Poland in 1655, and instead of fulfilling his vassal's duties towards the Polish Kingdom, by joining forces with the Swedes and subsequent treaties of Wehlau, Labiau, and Oliva, Elector and Duke Frederick William succeeded in revoking king of Poland's sovereignty over the Duchy of Prussia in 1660. The absolutist elector also subdued the noble estates of Prussia.
Document 3: Electorate of Cologne: The Electorate of Cologne (), sometimes referred to as Electoral Cologne (), was an ecclesiastical principality of the Holy Roman Empire that existed from the 10th to the early 19th century. It consisted of the Hochstift — the temporal possessions — of the Archbishop of Cologne and ruled by him in his capacity as prince-elector. There were only two other ecclesiastical prince-electors in the Empire: the Electorate of Mainz and the Electorate of Trier. The Archbishop-Elector of Cologne was also Arch-chancellor of Italy (one of the three component titular kingdoms of the Holy Roman Empire, the other two being Germany and Burgundy) and, as such, ranked second among all ecclesiastical and secular princes of the Empire, after the Archbishop-Elector of Mainz, and before that of Trier.
Document 4: Middle Ages: The coronation of Charlemagne as emperor on Christmas Day 800 is regarded as a turning point in medieval history, marking a return of the Western Roman Empire, since the new emperor ruled over much of the area previously controlled by the western emperors. It also marks a change in Charlemagne's relationship with the Byzantine Empire, as the assumption of the imperial title by the Carolingians asserted their equivalence to the Byzantine state. There were several differences between the newly established Carolingian Empire and both the older Western Roman Empire and the concurrent Byzantine Empire. The Frankish lands were rural in character, with only a few small cities. Most of the people were peasants settled on small farms. Little trade existed and much of that was with the British Isles and Scandinavia, in contrast to the older Roman Empire with its trading networks centred on the Mediterranean. The empire was administered by an itinerant court that travelled with the emperor, as well as approximately 300 imperial officials called counts, who administered the counties the empire had been divided into. Clergy and local bishops served as officials, as well as the imperial officials called missi dominici, who served as roving inspectors and troubleshooters.
Document 5: Greeks: The Eastern Roman Empire – today conventionally named the Byzantine Empire, a name not in use during its own time – became increasingly influenced by Greek culture after the 7th century, when Emperor Heraclius (AD 575 - 641) decided to make Greek the empire's official language. Certainly from then on, but likely earlier, the Roman and Greek cultures were virtually fused into a single Greco-Roman world. Although the Latin West recognized the Eastern Empire's claim to the Roman legacy for several centuries, after Pope Leo III crowned Charlemagne, king of the Franks, as the "Roman Emperor" on 25 December 800, an act which eventually led to the formation of the Holy Roman Empire, the Latin West started to favour the Franks and began to refer to the Eastern Roman Empire largely as the Empire of the Greeks (Imperium Graecorum).
Document 6: East Prussia: Although Brandenburg was a part of the Holy Roman Empire, the Prussian lands were not within the Holy Roman Empire and were with the administration by the Teutonic Order grandmasters under jurisdiction of the Emperor. In return for supporting Emperor Leopold I in the War of the Spanish Succession, Elector Frederick III was allowed to crown himself "King in Prussia" in 1701. The new kingdom ruled by the Hohenzollern dynasty became known as the Kingdom of Prussia. The designation "Kingdom of Prussia" was gradually applied to the various lands of Brandenburg-Prussia. To differentiate from the larger entity, the former Duchy of Prussia became known as Altpreußen ("Old Prussia"), the province of Prussia, or "East Prussia".
Document 7: Napoleon: After Austerlitz, Napoleon established the Confederation of the Rhine in 1806. A collection of German states intended to serve as a buffer zone between France and Central Europe, the creation of the Confederation spelled the end of the Holy Roman Empire and significantly alarmed the Prussians. The brazen reorganization of German territory by the French risked threatening Prussian influence in the region, if not eliminating it outright. War fever in Berlin rose steadily throughout the summer of 1806. At the insistence of his court, especially his wife Queen Louise, Frederick William III decided to challenge the French domination of Central Europe by going to war.
Document 8: Grand Duchy of Baden State Railway: The Grand Duchy of Baden was an independent state in what is now southwestern Germany until the creation of the German Empire in 1871. It had its own state-owned railway company, the Grand Duchy of Baden State Railways ("Großherzoglich Badische Staatseisenbahnen or G.Bad.St.E."), which was founded in 1840. At the time when it was integrated into the Deutsche Reichsbahn in 1920, its network had an overall length of about .
Document 9: Middle Ages: A three-year civil war followed his death. By the Treaty of Verdun (843), a kingdom between the Rhine and Rhone rivers was created for Lothair to go with his lands in Italy, and his imperial title was recognised. Louis the German was in control of Bavaria and the eastern lands in modern-day Germany. Charles the Bald received the western Frankish lands, comprising most of modern-day France. Charlemagne's grandsons and great-grandsons divided their kingdoms between their descendants, eventually causing all internal cohesion to be lost.[N] In 987 the Carolingian dynasty was replaced in the western lands, with the crowning of Hugh Capet (r. 987–996) as king.[O][P] In the eastern lands the dynasty had died out earlier, in 911, with the death of Louis the Child, and the selection of the unrelated Conrad I (r. 911–918) as king.
Document 10: Charlemagne: Charlemagne (/ ˈʃɑːrlɪmeɪn /) or Charles the Great (2 April 742 -- 28 January 814), numbered Charles I, was King of the Franks from 768, King of the Lombards from 774 and Emperor of the Romans from 800. He united much of Europe during the early Middle Ages. He was the first recognised emperor in western Europe since the fall of the Western Roman Empire three centuries earlier. The expanded Frankish state that Charlemagne founded is called the Carolingian Empire.
Document 11: Holy Roman Empire: The Holy Roman Empire (; ) was a multi-ethnic complex of territories in Western and Central Europe that developed during the Early Middle Ages and continued until its dissolution in 1806 during the Napoleonic Wars. The largest territory of the empire after 962 was the Kingdom of Germany, though it also came to include the neighboring Kingdom of Bohemia, the Kingdom of Burgundy, the Kingdom of Italy, and numerous other territories.
Document 12: Military history of France: Under Charlemagne the Franks reached the height of their power. After campaigns against Lombards, Avars, Saxons, and Basques, the resulting Carolingian Empire stretched from the Pyrenees to Central Germany, from the North Sea to the Adriatic. In 800 the Pope made Charlemagne Emperor of the West in return for protection of the Church. The Carolingian Empire was a conscious effort to recreate a central administration modeled on that of the Roman Empire,[13] but the motivations behind military expansion differed. Charlemagne hoped to provide his nobles an incentive to fight by encouraging looting on campaign. Plunder and spoils of war were stronger temptations than imperial expansion, and several regions were invaded over and over in order to bolster the coffers of Frankish nobility.[14] Cavalry dominated the battlefields, and while the high costs associated with equipping horses and horse-riders helped limit their numbers, Carolingian armies maintained an average size of 20,000 by recruiting infantry from imperial territories near theaters of operation.[15] The Empire lasted from 800 to 843, when, following Frankish tradition, it was split between the sons of Louis the Pious by the Treaty of Verdun.
Document 13: Electorate of Baden: The Electorate of Baden was a State of the Holy Roman Empire from 1803 to 1806. In 1803, Napoleon bestowed the office of Prince-elector to Charles Frederick. This only lasted until 1806, when Francis II dissolved the Empire. When the Holy Roman Empire dissolved, Baden achieved sovereignty, and Charles Frederick became Grand Duke.
Document 14: Holy Roman Empire: On 25 December 800, Pope Leo III crowned the Frankish king Charlemagne as Emperor, reviving the title in Western Europe, more than three centuries after the fall of the earlier ancient Western Roman Empire in 476. The title continued in the Carolingian family until 888 and from 896 to 899, after which it was contested by the rulers of Italy in a series of civil wars until the death of the last Italian claimant, Berengar I, in 924. The title was revived again in 962 when Otto I was crowned emperor, fashioning himself as the successor of Charlemagne and beginning a continuous existence of the empire for over eight centuries. Some historians refer to the coronation of Charlemagne as the origin of the empire, while others prefer the coronation of Otto I as its beginning. Scholars generally concur, however, in relating an evolution of the institutions and principles constituting the empire, describing a gradual assumption of the imperial title and role.
Document 15: Middle Ages: Charlemagne planned to continue the Frankish tradition of dividing his kingdom between all his heirs, but was unable to do so as only one son, Louis the Pious (r. 814–840), was still alive by 813. Just before Charlemagne died in 814, he crowned Louis as his successor. Louis's reign of 26 years was marked by numerous divisions of the empire among his sons and, after 829, civil wars between various alliances of father and sons over the control of various parts of the empire. Eventually, Louis recognised his eldest son Lothair I (d. 855) as emperor and gave him Italy. Louis divided the rest of the empire between Lothair and Charles the Bald (d. 877), his youngest son. Lothair took East Francia, comprising both banks of the Rhine and eastwards, leaving Charles West Francia with the empire to the west of the Rhineland and the Alps. Louis the German (d. 876), the middle child, who had been rebellious to the last, was allowed to keep Bavaria under the suzerainty of his elder brother. The division was disputed. Pepin II of Aquitaine (d. after 864), the emperor's grandson, rebelled in a contest for Aquitaine, while Louis the German tried to annex all of East Francia. Louis the Pious died in 840, with the empire still in chaos.
ground_truth: the Carolingian family
sub_queries: Electorate of Baden >> country Answer: Holy Roman Empire
dynasty that gave birth to Holy Roman Empire Answer: the Carolingian family